Maths Week 7 Graded Assignments IIT Madras

Maths week 7 graded assignment Complete 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

1.Table: M2W1G1 gives functions in Column A with their types in column B and their graphs in Column C.

Choose the options which represent the correct matching of a given function with its type and its graph.

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\to

\to

ii)

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\to

ii)

\to

\to

iii)

\to

\to

iii)

\to

\to

iv)

\to

\to

iv)

\to

\to

Yes, the answer is correct.
Score: 1

Accepted Answers:

\to

\to

ii)

\to

\to

iii)

\to

\to

iv)

\to

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1 point

2, Suppose $f (x)$ is a strictly increasing function and $g (x)$ is a strictly decreasing function. If the curves represented by $f (x)$ and $g (x)$ intersect at $x = x_{0}$ , then choose the set of correct options.

f (x) \geq g (x)

for all

x \geq x_{0}

There exists a point

x_{1} > x_{0}

such that

f (x_{1}) = g (x_{1})

g (x) \geq f (x)

for all

x \geq x_{0}

g (x) \geq f (x)

for all

x_{0} \geq x

f (x) \geq g (x)

for all

x_{0} \geq x

No, the answer is incorrect.
Score: 0

Accepted Answers:

f (x) \geq g (x)

for all

x \geq x_{0}

g (x) \geq f (x)

for all

x_{0} \geq x

3. Suppose $a_{n} = 3 n + 4 12 n ^{2} - n + 18 4 n ^{2} + 3$ . Find the value of $n \to \infty lim a_{n}$ (correct upto 2 decimal places).

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Range) 66.60,66.70

1 point

4. In the graphs given below, how many of the curves have a (unique) tangent at the origin (i.e., (0, 0))?

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Numeric) 2

0 points

Limits of some standard functions are given below:

$x \to 0 lim x l o g ( 1 + x ) = 1$
$x \to 0 lim x e ^{x} - 1 = 1$
$n \to \infty lim n (n ! 2 πn)^{n 1} = e$
$n \to \infty lim n n ! n = e$

Using the given information, find the value of

n \to \infty lim e n n! [l o g (1 + n 16) - ( 2 πn ) ^{n 1} ( e ^{(n 9)} - 1 )]

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Numeric) 7

1 point

6.Find the limit of the sequence given by $a_{n} = n ^{2} 3 + 5 + 7 + \dots + ( 2 n - 1 )$ , (where $n \in N ∖ {0}$ ).

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Numeric) 1

1 point

7. Find the value of $5 x \to 1 6^{+} lim ⌊ x ⌋ - 3 x \to 2^{-} lim ⌊ x ⌋$ , where $⌊ x ⌋$ denotes the greatest integer less than or equal to $x$ .

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Numeric) 77

1 point

8. Suppose a company runs three algorithms to estimate its future growth. Suppose the error in the estimation depends on the available number $(n)$ of data as follows:

Error in estimation by Algorithm 1: $a_{n} = 6 n ^{2} + 1 n ^{2} + 5 n$ .
Error in estimation by Algorithm 2: $b_{n} = 8 1 + (- 1)^{n} n 1$
Error in estimation by Algorithm 3: $c_{n} = 7 e ^{n} e ^{n} + 4$

where $n \in N ∖ {0}$ .Suppose the company has a large amount of data in hand (we can assume $n$ tends to $\infty$ ). Using the information given above, answer the questions below.

1 point

Which of the following statements is (are) correct?

Error in estimation by Algorithm 2 will be 0.500.

Error in estimation by Algorithm 2 will give the minimum error.

Error in estimation by Algorithm 2 will give the maximum error.

Both Algorithm 1 and Algorithm 2 will give the same error and that will be the maximum.

Error in estimation by Algorithm 1 will be 0.166 approximately.

No, the answer is incorrect.
Score: 0

Accepted Answers:

Error in estimation by Algorithm 2 will give the minimum error.

Error in estimation by Algorithm 1 will be 0.166 approximately.

1 point

9. Suppose a new algorithm is designed to predict the growth of the company in future and the error in estimation by the new algorithm is given by $a_{n} - b_{n}$ , where $a_{n}$ and $b_{n}$ are the same as defined earlier. Choose the set of correct options.

The error in estimation using the new algorithm is less than the error in estimation using Algorithm 1.

The error in estimation using Algorithm 2 is less than the error in estimation using the new algorithm.

The error in estimation using the new algorithm is less than the error in estimation using Algorithm 3.

The error in estimation using the new algorithm cannot be compared with the error in estimation using Algorithm 3.

Yes, the answer is correct.
Score: 1

Accepted Answers:

The error in estimation using the new algorithm is less than the error in estimation using Algorithm 1.

The error in estimation using the new algorithm is less than the error in estimation using Algorithm 3.

10.Suppose the company modified the error in estimation by Algorithm 3 as $c_{n}^{^{'}} = n e^{(12 n 1)} - n$ .
What will be the new error in estimation by Algorithm 3? (Correct upto 3 decimal places)

No, the answer is incorrect.
Score: 0

Accepted Answers:

(Type: Numeric) 0.083

Graded Assignments Full Solutions PDF

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Maths Week 7 Graded Assignments IIT Madras

1.Table: M2W1G1 gives functions in Column A with their types in column B and their graphs in Column C.Choose the options which represent the correct matching of a given function with its type and its graph.

Yes, the answer is correct.Score: 1

Accepted Answers:

2, Suppose �(�)f(x) is a strictly increasing function and �(�)g(x) is a strictly decreasing function. If the curves represented by �(�)f(x) and �(�)g(x) intersect at �=�0x=x0, then choose the set of correct options.

No, the answer is incorrect.Score: 0

Accepted Answers:

3. Suppose ��=12�23�+4−4�2+3�+18an=3n+412n2−n+184n2+3. Find the value of lim⁡�→∞��n→∞liman (correct upto 2 decimal places).

No, the answer is incorrect.Score: 0

Accepted Answers:

4. In the graphs given below, how many of the curves have a (unique) tangent at the origin (i.e., (0, 0))?

No, the answer is incorrect.Score: 0

Accepted Answers:

No, the answer is incorrect.Score: 0

Accepted Answers:

6.Find the limit of the sequence given by ��=3+5+7+…+(2�−1)�2an=n23+5+7+…+(2n−1), (where �∈�∖{0}n∈N∖{0}).

No, the answer is incorrect.Score: 0

Accepted Answers:

7. Find the value of 5lim⁡�→16+⌊�⌋−3lim⁡�→2−⌊�⌋5x→16+lim⌊x⌋−3x→2−lim⌊x⌋, where ⌊�⌋⌊x⌋ denotes the greatest integer less than or equal to �x.

No, the answer is incorrect.Score: 0

Accepted Answers:

8. Suppose a company runs three algorithms to estimate its future growth. Suppose the error in the estimation depends on the available number (�)(n) of data as follows:

No, the answer is incorrect.Score: 0

Accepted Answers:

9. Suppose a new algorithm is designed to predict the growth of the company in future and the error in estimation by the new algorithm is given by ��−��an−bn, where ��an and ��bn are the same as defined earlier. Choose the set of correct options.

Yes, the answer is correct.Score: 1

Accepted Answers:

10.Suppose the company modified the error in estimation by Algorithm 3 as ��′=��(112�)−�cn′=ne(12n1)−n.What will be the new error in estimation by Algorithm 3? (Correct upto 3 decimal places)

No, the answer is incorrect.Score: 0

Accepted Answers:

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1.Table: M2W1G1 gives functions in Column A with their types in column B and their graphs in Column C.

Choose the options which represent the correct matching of a given function with its type and its graph.

Yes, the answer is correct.
Score: 1

2, Suppose $f (x)$ is a strictly increasing function and $g (x)$ is a strictly decreasing function. If the curves represented by $f (x)$ and $g (x)$ intersect at $x = x_{0}$ , then choose the set of correct options.

No, the answer is incorrect.
Score: 0

3. Suppose $a_{n} = 3 n + 4 12 n ^{2} - n + 18 4 n ^{2} + 3$ . Find the value of $n \to \infty lim a_{n}$ (correct upto 2 decimal places).

No, the answer is incorrect.
Score: 0

No, the answer is incorrect.
Score: 0

No, the answer is incorrect.
Score: 0

6.Find the limit of the sequence given by $a_{n} = n ^{2} 3 + 5 + 7 + \dots + ( 2 n - 1 )$ , (where $n \in N ∖ {0}$ ).

No, the answer is incorrect.
Score: 0

7. Find the value of $5 x \to 1 6^{+} lim ⌊ x ⌋ - 3 x \to 2^{-} lim ⌊ x ⌋$ , where $⌊ x ⌋$ denotes the greatest integer less than or equal to $x$ .

No, the answer is incorrect.
Score: 0

8. Suppose a company runs three algorithms to estimate its future growth. Suppose the error in the estimation depends on the available number $(n)$ of data as follows:

No, the answer is incorrect.
Score: 0

9. Suppose a new algorithm is designed to predict the growth of the company in future and the error in estimation by the new algorithm is given by $a_{n} - b_{n}$ , where $a_{n}$ and $b_{n}$ are the same as defined earlier. Choose the set of correct options.

Yes, the answer is correct.
Score: 1

10.Suppose the company modified the error in estimation by Algorithm 3 as $c_{n}^{^{'}} = n e^{(12 n 1)} - n$ .
What will be the new error in estimation by Algorithm 3? (Correct upto 3 decimal places)

No, the answer is incorrect.
Score: 0