Test: Theorems of Integral Calculus- 1 - Civil Engineering (CE) MCQ

# Test: Theorems of Integral Calculus- 1 - Civil Engineering (CE) MCQ

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

Test: Theorems of Integral Calculus- 1 for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation. The Test: Theorems of Integral Calculus- 1 questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Theorems of Integral Calculus- 1 MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Theorems of Integral Calculus- 1 below.
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Test: Theorems of Integral Calculus- 1 - Question 1

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

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Test: Theorems of Integral Calculus- 1 - Question 2
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Test: Theorems of Integral Calculus- 1 - Question 3
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Given

Square both side, we get

Test: Theorems of Integral Calculus- 1 - Question 4

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Test: Theorems of Integral Calculus- 1 - Question 5

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cos x and sin x are finite whatever x may be

Test: Theorems of Integral Calculus- 1 - Question 6

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Test: Theorems of Integral Calculus- 1 - Question 7

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

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Test: Theorems of Integral Calculus- 1 - Question 8

If f(x) =    then limx-►3 f(x) will be

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Test: Theorems of Integral Calculus- 1 - Question 9

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= 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?

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By the given condition

From (1), λ = 1

Test: Theorems of Integral Calculus- 1 - Question 11

The value of the function

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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

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Test: Theorems of Integral Calculus- 1 - Question 13

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

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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

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Test: Theorems of Integral Calculus- 1 - Question 16

The integral    is given by

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Test: Theorems of Integral Calculus- 1 - Question 17

Which one of the following function is strictly bounded?

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

Test: Theorems of Integral Calculus- 1 - Question 18

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Test: Theorems of Integral Calculus- 1 - Question 19

Which of the following integrals is unbounded?

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Test: Theorems of Integral Calculus- 1 - Question 20

What is the value of the definite integral,

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