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Test: Theorems of Integral Calculus- 1 - Mechanical Engineering MCQ


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20 Questions MCQ Test GATE Mechanical (ME) 2024 Mock Test Series - Test: Theorems of Integral Calculus- 1

Test: Theorems of Integral Calculus- 1 for Mechanical Engineering 2024 is part of GATE Mechanical (ME) 2024 Mock Test Series preparation. The Test: Theorems of Integral Calculus- 1 questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: Theorems of Integral Calculus- 1 MCQs are made for Mechanical Engineering 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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