Test: Theorems of Integral Calculus- 1

# Test: Theorems of Integral Calculus- 1

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Test: Theorems of Integral Calculus- 1 - Question 1

### As x is increased from – ∞ to ∞ , the function Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 1 Test: Theorems of Integral Calculus- 1 - Question 2

### Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 2 Test: Theorems of Integral Calculus- 1 - Question 3

### Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 3

Given  Square both side, we get     Test: Theorems of Integral Calculus- 1 - Question 4 Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 4   Test: Theorems of Integral Calculus- 1 - Question 5 Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 5

cos x and sin x are finite whatever x may be  Test: Theorems of Integral Calculus- 1 - Question 6 Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 6 Test: Theorems of Integral Calculus- 1 - Question 7

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

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 7 Test: Theorems of Integral Calculus- 1 - Question 8

If f(x) = then limx-►3 f(x) will be

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 8   Test: Theorems of Integral Calculus- 1 - Question 9 Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 9  = 1/12

Test: Theorems of Integral Calculus- 1 - Question 10

What should be the value of λ such that the function defined below is continuous at x = π/2? Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 10

By the given condition  From (1), λ = 1

Test: Theorems of Integral Calculus- 1 - Question 11

The value of the function Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 11 Test: Theorems of Integral Calculus- 1 - Question 12

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

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 12 Test: Theorems of Integral Calculus- 1 - Question 13

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

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 13 Test: Theorems of Integral Calculus- 1 - 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?

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 14 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.

Test: Theorems of Integral Calculus- 1 - Question 15

What is the value of Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 15   Test: Theorems of Integral Calculus- 1 - Question 16

The integral is given by

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 16     Test: Theorems of Integral Calculus- 1 - Question 17

Which one of the following function is strictly bounded?

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 17

For a strictly bounded function f(x), limit should be finite Test: Theorems of Integral Calculus- 1 - Question 18 Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 18    Test: Theorems of Integral Calculus- 1 - Question 19

Which of the following integrals is unbounded?

Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 19 Test: Theorems of Integral Calculus- 1 - Question 20

What is the value of the definite integral, Detailed Solution for Test: Theorems of Integral Calculus- 1 - Question 20      ## GATE Mechanical (ME) 2023 Mock Test Series

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