{"id":880,"date":"2023-08-11T17:56:47","date_gmt":"2023-08-11T12:26:47","guid":{"rendered":"https:\/\/iitmadrasstudentscommunity.me\/?p=880"},"modified":"2023-08-11T18:01:53","modified_gmt":"2023-08-11T12:31:53","slug":"maths-week-8-graded-assignments-iit-madras","status":"publish","type":"post","link":"https:\/\/iitmadrasstudentscommunity.me\/maths-week-8-graded-assignments-iit-madras\/","title":{"rendered":"Maths Week 8 Graded Assignments IIT Madras"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"880\" class=\"elementor elementor-880\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-80ee2dc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"80ee2dc\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-83e6ef7\" data-id=\"83e6ef7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-82ab21b elementor-widget elementor-widget-text-editor\" data-id=\"82ab21b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><em style=\"font-family: 'Trebuchet MS', sans-serif;\">Maths week 8 graded assignment Complete\u00a0 Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments\u00a0<\/em><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6877206 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6877206\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0fa777c\" data-id=\"0fa777c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c4d472b elementor-widget elementor-widget-text-editor\" data-id=\"c4d472b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"3E9iw3CT2Eu4\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div id=\"3E9iw3CT2Eu4.0.6616104164130816\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">1.Match the given functions in Column A with the equations of their tangents at the origin\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">(0,0)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0in column B and the plotted graphs and the tangents in Column C, given in Table M2W2G1.<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px; padding: 0px; vertical-align: middle;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t3_ma1003\/assets\/img\/T3M2W2.jpg\" alt=\"\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.0.6616104164130816.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.0.6616104164130816\" type=\"checkbox\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.0\">ii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0a)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.0.6616104164130816.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.0.6616104164130816\" type=\"checkbox\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.1\">i)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0b)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a03.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.0.6616104164130816.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.0.6616104164130816\" type=\"checkbox\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.2\">iii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0b)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.0.6616104164130816.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.0.6616104164130816\" type=\"checkbox\" data-index=\"3\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.3\">iii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0c)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a02.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.0.6616104164130816.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.0.6616104164130816\" type=\"checkbox\" data-index=\"4\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.4\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.4\">i)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0a)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.0\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.0\">ii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0a)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a01.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.1\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.1\">i)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0b)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a03.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.3\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.0.6616104164130816.3\">iii)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a0c)\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2192<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><\/span><\/span><\/span>\u00a02.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"3E9iw3CT2Eu4.1.6053154210709504\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">2.Consider the following two functions\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>.<\/h4><h4>\u00a0<\/h4><h4>\u00a0<\/h4><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={\ufffd3\u22129\ufffd\ufffd(\ufffd\u22123)if\u00a0\ufffd\u22600,33if\u00a0\ufffd=00if\u00a0\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.35002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.19999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.60002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.45896em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.45896em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.01792em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mopen mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mclose mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.891314em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.931em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord vbox\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; align-items: baseline; display: inline-flex; flex-direction: column;\"><span class=\"thinbox\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-flex; flex-direction: row; max-width: 0px; width: 0px;\"><span class=\"rlap\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; width: 0px;\"><span class=\"inner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: absolute; left: 0px;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.93096em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.49096em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={\u2223\ufffd\u2223if\u00a0\ufffd\u22642\u230a\ufffd\u230bif\u00a0\ufffd&gt;2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen delimcenter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; top: 0em;\"><span class=\"delimsizing size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">{<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u230a<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u230b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>Choose the set of correct options.<\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.1.6053154210709504.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.1.6053154210709504\" type=\"checkbox\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is discontinuous at both\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.1.6053154210709504.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.1.6053154210709504\" type=\"checkbox\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is discontinuous only at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.1.6053154210709504.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.1.6053154210709504\" type=\"checkbox\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is discontinuous only at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.1.6053154210709504.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.1.6053154210709504\" type=\"checkbox\" data-index=\"3\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is discontinuous at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.1.6053154210709504.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.1.6053154210709504\" type=\"checkbox\" data-index=\"4\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.4\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.4\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is discontinuous at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.2\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is discontinuous only at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.4\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.1.6053154210709504.4\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is discontinuous at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><h4 class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">3.<\/h4><div id=\"3E9iw3CT2Eu4.2.6053510290341888\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">Consider the graphs given below:<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><img decoding=\"async\" class=\"yui-img\" style=\"margin: 0px; padding: 0px; vertical-align: middle;\" title=\"\" src=\"https:\/\/backend.seek.onlinedegree.iitm.ac.in\/21t3_ma1003\/assets\/img\/T3M2W2-1.jpg\" alt=\"\" \/><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>Choose the set of correct options from the below.<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.2.6053510290341888.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.2.6053510290341888\" type=\"checkbox\" data-index=\"0\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.0\">Curve 1 is both continuous and differentiable at the origin.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.2.6053510290341888.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.2.6053510290341888\" type=\"checkbox\" data-index=\"1\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.1\">Curve 2 is continuous but not differentiable at the origin.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.2.6053510290341888.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.2.6053510290341888\" type=\"checkbox\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.2\">Curve 2 has derivative 0 at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.2.6053510290341888.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.2.6053510290341888\" type=\"checkbox\" data-index=\"3\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.3\">Curve 3 is continuous but not differentiable at the origin.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.2.6053510290341888.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.2.6053510290341888\" type=\"checkbox\" data-index=\"4\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.4\">Curve 4 is not differentiable anywhere.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"3E9iw3CT2Eu4.2.6053510290341888.5\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"3E9iw3CT2Eu4.2.6053510290341888\" type=\"checkbox\" data-index=\"5\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.5\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.5\">Curve 4 has derivative 0 at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.0\">Curve 1 is both continuous and differentiable at the origin.<\/label><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.2\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.2\">Curve 2 has derivative 0 at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><label style=\"margin: 0px; padding: 0px;\" for=\"3E9iw3CT2Eu4.2.6053510290341888.3\">Curve 3 is continuous but not differentiable at the origin.<\/label><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"hHkZOzR9ntSG\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"hHkZOzR9ntSG.0.5490204257288192\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">4.Choose the set of correct options considering the function given below:<\/h4><h4>\u00a0<\/h4><h4>\u00a0<\/h4><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={\ufffd\ufffd\ufffd\u00a0\ufffd\ufffdif\u00a0\ufffd\u22600,1if\u00a0\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen delimcenter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; top: 0em;\"><span class=\"delimsizing size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">{<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.855664em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">s<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">in<\/span><span class=\"mspace nobreak mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0<\/span><\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord vbox\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; align-items: baseline; display: inline-flex; flex-direction: column;\"><span class=\"thinbox\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-flex; flex-direction: row; max-width: 0px; width: 0px;\"><span class=\"rlap\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; width: 0px;\"><span class=\"inner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: absolute; left: 0px;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.0.5490204257288192.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.0.5490204257288192\" type=\"checkbox\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is not continuous at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.0.5490204257288192.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.0.5490204257288192\" type=\"checkbox\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.0.5490204257288192.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.0.5490204257288192\" type=\"checkbox\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is not differentiable at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.0.5490204257288192.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.0.5490204257288192\" type=\"checkbox\" data-index=\"3\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is differentiable at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.0.5490204257288192.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.0.5490204257288192\" type=\"checkbox\" data-index=\"4\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.4\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.4\">The derivative of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>\u00a0(if exists) is\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.0.5490204257288192.5\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.0.5490204257288192\" type=\"checkbox\" data-index=\"5\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.5\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.5\">The derivative of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>\u00a0(if exists) is\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">1<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.1\"><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.3\"><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is differentiable at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.4\"><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.0.5490204257288192.4\">The derivative of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>\u00a0(if exists) is\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"hHkZOzR9ntSG.1.4869660570812416\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">5. Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><\/span><\/span><\/span><\/span>\u00a0be a polynomial of degree 5, which is given by<\/h4><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)=\ufffd5\ufffd5+\ufffd4\ufffd4+\ufffd3\ufffd3+\ufffd2\ufffd2+\ufffd1\ufffd+\ufffd0.<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">.<\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2032(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">b<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0denote the derivative of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><\/span><\/span><\/span><\/span>\u00a0at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">b<\/span><\/span><\/span><\/span><\/span>. Choose the set of correct options.<\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.1.4869660570812416.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.1.4869660570812416\" type=\"checkbox\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd1=\ufffd\u2032(0)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.1.4869660570812416.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.1.4869660570812416\" type=\"checkbox\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">5\ufffd5+3\ufffd3=12(\ufffd\u2032(1)+\ufffd\u2032(\u22121)\u22122\ufffd\u2032(0))<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">))<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.1.4869660570812416.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.1.4869660570812416\" type=\"checkbox\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">4\ufffd4+2\ufffd2=12(\ufffd\u2032(1)\u2212\ufffd\u2032(\u22121))<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">))<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"hHkZOzR9ntSG.1.4869660570812416.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" disabled=\"disabled\" name=\"hHkZOzR9ntSG.1.4869660570812416\" type=\"checkbox\" data-index=\"3\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.3\">None of the above.<\/label><\/div><\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.0\"><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd1=\ufffd\u2032(0)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.1\"><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">5\ufffd5+3\ufffd3=12(\ufffd\u2032(1)+\ufffd\u2032(\u22121)\u22122\ufffd\u2032(0))<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">))<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.2\"><label style=\"margin: 0px; padding: 0px;\" for=\"hHkZOzR9ntSG.1.4869660570812416.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">4\ufffd4+2\ufffd2=12(\ufffd\u2032(1)\u2212\ufffd\u2032(\u22121))<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">a<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">))<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"hHkZOzR9ntSG.2.4965924746559488\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">6. Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><\/span><\/span><\/span><\/span>\u00a0be a differentiable function at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span>. The tangent line to the graph of the function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><\/span><\/span><\/span><\/span>\u00a0at the point\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">(3,0)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>, passes through the point\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">(5,4)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>. What will be the value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2032(3)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>?<\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) 2<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"hHkZOzR9ntSG.3.5441571939942400\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">7. Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><\/span><\/span><\/span><\/span>\u00a0be two functions which are differentiable at each\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2208\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2208<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span>. Suppose that,\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)=\ufffd(\ufffd2+5\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>, and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2032(0)=10<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">10<\/span><\/span><\/span><\/span><\/span>. Find the value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2032(0)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>.<\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) 2<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"KknoVK2zVNED\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"KknoVK2zVNED.0.5025969832198144\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">8. Consider a function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd:\ufffd\u2192\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">:<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span>\u00a0defined as\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={sin\u206112\ufffd+\ufffdsin\u2061\ufffd15\ufffd3if\u00a0\ufffd\u22600,\ufffdif\u00a0\ufffd=0.<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen delimcenter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; top: 0em;\"><span class=\"delimsizing size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">{<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.872331em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">15<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.746314em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.786em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">s<\/span><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">i<\/span><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">n<\/span><\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">12<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><span class=\"mop mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">s<\/span><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">i<\/span><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">n<\/span><\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord vbox\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; align-items: baseline; display: inline-flex; flex-direction: column;\"><span class=\"thinbox\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-flex; flex-direction: row; max-width: 0px; width: 0px;\"><span class=\"rlap\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; width: 0px;\"><span class=\"inner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: absolute; left: 0px;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0If\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.10764em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">f<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous at\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>\u00a0, then find the value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">90\ufffd\u2212\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">90<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><\/span><\/span><\/span><\/span><\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-KknoVK2zVNED.0.5025969832198144\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" disabled=\"disabled\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) -1704<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"pE2Lf9VuwItx\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"pE2Lf9VuwItx.0.6237863876231168\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">9. The distance (in meters) traveled by a car after\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><\/span><\/span><\/span><\/span>\u00a0minutes is given by the function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)=\ufffd(6\ufffd3+5\ufffd2+8\ufffd+5)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">d<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0, where\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><\/span><\/span><\/span><\/span>\u00a0is a differentiable function with domain\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span>\u00a0. Find the instantaneous speed of the car after 5 min, where\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2032(920)=2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.751892em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">920<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) 1016<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"9Ct8BejEie6n\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"9Ct8BejEie6n.0.5144101162844160\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">10. Consider the following two functions<\/h4><h4>\u00a0<\/h4><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd:\ufffd\u2192\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">:<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span>\u00a0<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={6\ufffd(\ufffd\u22125)\u22126\ufffd\u22125if\u00a00\u2264\ufffd&lt;5,6\ufffd=56(\ufffd2\u221225)1ln\u2061(\ufffd\u22125)if\u00a0\ufffd&gt;5<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.35002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.19999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.60002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.47496em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.47948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.0707em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.966714em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.96671em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mclose mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.03948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53226em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">25<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.07522em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.4842em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.844314em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.64079em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">l<\/span><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">n<\/span><\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mclose mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.384em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.47496em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.47948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.03948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53226em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>and<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd:\ufffd\u2192\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">:<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)=\u2223\ufffd(\ufffd\u22125)(\ufffd\u22128)\u2223<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223<\/span><\/span><\/span><\/span><\/span>\u00a0and the following statements (a function is said to be continuous (respectively differentiable) if it is continuous (respectively differentiable) at all the points in the domain of the function).<br style=\"margin: 0px; padding: 0px;\" \/>\u00a0<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0P:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0P:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0Both the functions\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0are continuous.<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0Q:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0Q:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0Both the functions\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0are not differentiable.<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0R:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0R:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous,\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is differentiable.<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0S:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0S:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous,\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is not differentiable.<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0T:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0T:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0Neither\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0nor\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous.<br style=\"margin: 0px; padding: 0px;\" \/>\u00a0<br style=\"margin: 0px; padding: 0px;\" \/>Find the number of correct statements.<\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) 2<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"PE6IZe6lfVwm\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"PE6IZe6lfVwm.0.5842047978176512\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>11. Consider the following function<\/div><div>\u00a0<\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd:\ufffd\u2192\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">:<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span>\u00a0<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={8\ufffd(\ufffd\u22125)\u22128\ufffd\u22125if\u00a00\u2264\ufffd&lt;5,8\ufffd=58(\ufffd2\u221225)1ln\u2061(\ufffd\u22125)if\u00a0\ufffd&gt;5<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.35002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.19999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.60002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.47496em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.47948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.0707em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.966714em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.96671em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mclose mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.03948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53226em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">25<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.07522em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.4842em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.844314em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.64079em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">l<\/span><span class=\"mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">n<\/span><\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mclose mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.384em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.47496em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.47948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.03948em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53226em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>If linear function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\ufffd(\ufffd)=\ufffd\ufffd+\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">L<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.151392em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><\/span><\/span><\/span><\/span>\u00a0denotes the best linear approximation of the function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0at the point\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=1<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>, find the value of<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u22128\ufffd\u22124\u22121(\ufffd+\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.746314em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.786em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) 16<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"nxC9GVEHs86t\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"nxC9GVEHs86t.0.5019359474876416\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><h4 class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">12. Consider the following function<br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd:\ufffd\u2192\ufffd\ufffd(\ufffd)=\u2223\ufffd(\ufffd\u22122)(\ufffd\u22128)\u2223.<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">:<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2223.<\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>If\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">m<\/span><\/span><\/span><\/span><\/span>\u00a0is slope of the tangent of the function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0at point\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=32<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, find the value\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u2212274<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">m<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">27<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h4><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) -14<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\">The population of a bacteria culture of type A in laboratory conditions is known to be a function of time of the form<\/span><\/p><p>\u00a0<\/p><p><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd:\ufffd\u2192\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">:<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={\ufffd3\u221227\ufffd\u22123if\u00a00\u2264\ufffd&lt;3,27\ufffd=31\ufffd81(\ufffd\u22123)(\ufffd27\ufffd\u2212\ufffd81)if\u00a0\ufffd&gt;3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.35002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.19999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.60002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.45896em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.45896em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.01792em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.891314em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.931em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">27<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01896em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">27<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.57896em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.845108em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.746314em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.786em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">81<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mclose mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">27<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">81<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.45896em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.45896em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.01896em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.57896em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\">where\u00a0<\/span><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\">\u00a0represents the population (in lakhs) and\u00a0<\/span><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><\/span><\/span><\/span><\/span><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"> represents the time (in minutes). The population of a bacteria culture of type B in laboratory conditions is known to be a function of time of the forM<\/span><\/p><p>\u00a0<\/p><p>\u00a0<\/p><p><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd:\ufffd\u2192\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">:<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2192<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathbb\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_AMS;\">R<\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)={(5\ufffd\u22129)1\ufffd\u22122if\u00a00\u2264\ufffd&lt;2,\ufffd4\ufffd=2\ufffd\ufffd+2\u2212\ufffd4\ufffd\u22122if\u00a0\ufffd&gt;2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.35002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.19999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.60002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.41496em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.42488em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.981235em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.39022em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.844314em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.656em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.384em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.98488em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53496em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.01792em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.655em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.394em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.891314em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.931em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.891314em;\"><span class=\"\" style=\"margin: 0px 0.0714286em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.931em;\"><span class=\"sizing reset-size3 size1 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.714286em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 2.41496em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.42488em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.98488em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53496em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\">where\u00a0<\/span><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\">\u00a0represents the population (in lakhs) and\u00a0<\/span><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><\/span><\/span><\/span><\/span><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\">\u00a0represents the time (in minutes).<\/span><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><br style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\" \/><span style=\"color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\">Using the information above, answer questions 13,14 and 15.<\/span><\/p><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"DRysL4LvI5z0\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"DRysL4LvI5z0.0.4647386483785728\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>Consider the following statements (a function is said to be continuous if it is continuous at all the points in the domain of the function).<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0P:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0P:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0Both the functions\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0are continuous.<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0Q:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0Q:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous, but\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is not.<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0R:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0R:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous, but\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is not.<br style=\"margin: 0px; padding: 0px;\" \/><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">Statement\u00a0S:<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord textbf\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-weight: bold;\">Statement\u00a0S:<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0Neither\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0nor\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0is continuous.<br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0Find the number of the correct statements.<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) 1<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"DRysL4LvI5z0.1.4601129149136896\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>If\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\ufffd(\ufffd)=\ufffd\ufffd+\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">L<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.151392em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><\/span><\/span><\/span><\/span>\u00a0denotes the best linear approximation of the function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0at the point\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=1<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>, then find the value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">2\ufffd+\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><\/span><\/span><\/span><\/span>.<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) 18<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"DRysL4LvI5z0.2.5983141546164224\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>If\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\ufffd(\ufffd)=\ufffd4(\ufffd\ufffd+\ufffd)+\ufffd\ufffd5<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">L<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.151392em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">C<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">e<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0denotes the best linear approximation of the function\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">q<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>\u00a0at the point\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=3<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span>, then find the value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd+\ufffd+\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">C<\/span><\/span><\/span><\/span><\/span>.<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; letter-spacing: normal;\"><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">No, the answer is incorrect.<\/span><br style=\"margin: 1rem 0px; padding: 0px;\" \/><span class=\"incorrect\" style=\"margin: 1rem 0px; padding: 0px; color: #ff3b3b;\">Score: 0<\/span><\/h3><div style=\"margin: 0px; padding: 0px;\"><h3 class=\"feedback-header faculty-answer\" style=\"margin-bottom: 16px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 400; font-stretch: normal; font-size: 16px; line-height: 28px; font-family: Roboto, 'Helvetica Neue', sans-serif; color: #05a660; letter-spacing: normal;\">Accepted Answers:<\/h3><div class=\"faculty-answer\" style=\"margin: 0px; padding: 0px; color: #05a660;\">(Type: Numeric) -2<\/div><\/div><\/div><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div><em style=\"margin: 0px; padding: 0px;\">\u00a0<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a8e0abf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a8e0abf\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7eb41c2\" data-id=\"7eb41c2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a5c458e elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"a5c458e\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/drive.google.com\/drive\/folders\/14b4zsoM_A6QFwFZudJjC8I4Fgu-Navb1?usp=drive_link\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Graded Assignments Full Solutions PDF <\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3b5881c elementor-share-buttons--view-icon-text elementor-share-buttons--skin-gradient elementor-share-buttons--shape-square elementor-grid-0 elementor-share-buttons--color-official elementor-widget elementor-widget-share-buttons\" data-id=\"3b5881c\" data-element_type=\"widget\" data-widget_type=\"share-buttons.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<link rel=\"stylesheet\" href=\"https:\/\/iitmadrasstudentscommunity.me\/wp-content\/plugins\/elementor-pro\/assets\/css\/widget-share-buttons.min.css\">\t\t<div class=\"elementor-grid\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-grid-item\">\n\t\t\t\t\t\t<div\n\t\t\t\t\t\t\tclass=\"elementor-share-btn elementor-share-btn_whatsapp\"\n\t\t\t\t\t\t\trole=\"button\"\n\t\t\t\t\t\t\ttabindex=\"0\"\n\t\t\t\t\t\t\taria-label=\"Share on whatsapp\"\n\t\t\t\t\t\t>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-share-btn__icon\">\n\t\t\t\t\t\t\t\t<i class=\"fab fa-whatsapp\" aria-hidden=\"true\"><\/i>\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-share-btn__text\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span 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Or For Some Others Reasons Not Able To Complete Graded Assignments\u00a0 1.Match the given functions in Column A with the equations of their tangents at the origin\u00a0(0,0)(0,0)\u00a0in column B and the plotted&hellip;&nbsp;<a href=\"https:\/\/iitmadrasstudentscommunity.me\/maths-week-8-graded-assignments-iit-madras\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Maths Week 8 Graded Assignments IIT Madras<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":882,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","neve_meta_reading_time":"","_themeisle_gutenberg_block_has_review":false,"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"categories":[10],"tags":[],"_links":{"self":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/880"}],"collection":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/comments?post=880"}],"version-history":[{"count":4,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/880\/revisions"}],"predecessor-version":[{"id":888,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/880\/revisions\/888"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media\/882"}],"wp:attachment":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media?parent=880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/categories?post=880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/tags?post=880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}