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Test: Theorems of Integral Calculus- 1

20 Questions MCQ Test Engineering Mathematics | Test: Theorems of Integral Calculus- 1

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Attempt Test: Theorems of Integral Calculus- 1 | 20 questions in 60 minutes | Mock test for GATE preparation | Free important questions MCQ to study Engineering Mathematics for GATE Exam | Download free PDF with solutions
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 limx-►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:       Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code

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