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QUESTION: 1

As x is increased from – ∞ to ∞ , the function

Solution:

QUESTION: 2

Solution:

QUESTION: 3

Solution:

Given

Square both side, we get

QUESTION: 4

Solution:

QUESTION: 5

Solution:

cos x and sin x are finite whatever x may be

QUESTION: 6

Solution:

QUESTION: 7

Which of the following functions is not differentiable in the domain [-1,1]?

Solution:

QUESTION: 8

If f(x) = then lim_{x-►3} f(x) will be

Solution:

QUESTION: 9

Solution:

= 1/12

QUESTION: 10

What should be the value of λ such that the function defined below is continuous at x = π/2?

Solution:

By the given condition

From (1), λ = 1

QUESTION: 11

The value of the function

Solution:

QUESTION: 12

Consider the function f(x) = |x|^{3}, where x is real. Then the function f(x) at x = 0 is

Solution:

QUESTION: 13

The expression e^{–ln x} for x > 0 is equal to

Solution:

QUESTION: 14

Consider the following two statements about the function f(x) = |x|

P: f(x) is continuous for all real values of x

Q: f(x) is differentiable for all real values of x

Which of the f oll owi ng is TRU E?

Solution:

The graph of f(x) is

f(x) is continuous for all real values of x Lim |x| = Lim |x| = 0

as can be seen from graph of |x|.

and Lim f(x) = +1 as can be seen from graph of |x|

x → 0+

Left deriva tive ≠ Rig ht derivative

So |x| is continuous but not differentiable at x = 0.

QUESTION: 15

What is the value of

Solution:

QUESTION: 16

The integral is given by

Solution:

QUESTION: 17

Which one of the following function is strictly bounded?

Solution:

For a strictly bounded function f(x), limit should be finite

QUESTION: 18

Solution:

QUESTION: 19

Which of the following integrals is unbounded?

Solution:

QUESTION: 20

What is the value of the definite integral,

Solution:

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