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NDA || Mathematics || Calculus || Continuity and Differentiability || Quiz 2020

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Question 1

For

Question 2

Consider the following statements:

1) If and both exist, then  exists.

2) If exists, then both and  must exist.

Which of the above statements is/are correct?

Question 3

Consider the following statements:

1) The function f(x) = x2 + 2 cos x is increasing in the interval (0, π)

2) The function  is decreasing in the interval (-∞, ∞)

Which of the above statements is/are correct?

Question 4

Let then

Question 5

The function  in the interval  is,

Question 6

Suppose the function , is differentiable for all x.Then n can be any element of the interval

Question 7

Consider the following statements :

1) Derivative of  may not exist at some point.

2) Derivative of  may exist finitely at some point.

3) Derivative of  may be infinite (geometrically) at some point.

Which of the above statements are correct?

Question 8

If  then  is

Question 9

The function  is not defined at x = π. The value of f(π) so that f(x) is continuous at x = π is

Question 10

Consider the following functions:

1)

2)

Which of the above function is/are derivable at x = 0?

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