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Test: Theorems of Integral Calculus- 2 - Mechanical Engineering MCQ


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20 Questions MCQ Test GATE Mechanical (ME) 2024 Mock Test Series - Test: Theorems of Integral Calculus- 2

Test: Theorems of Integral Calculus- 2 for Mechanical Engineering 2024 is part of GATE Mechanical (ME) 2024 Mock Test Series preparation. The Test: Theorems of Integral Calculus- 2 questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: Theorems of Integral Calculus- 2 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- 2 below.
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Test: Theorems of Integral Calculus- 2 - Question 1

A function is given by f(t) = sin2t + cos 2t. Which of the following is true?  

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Test: Theorems of Integral Calculus- 2 - Question 2

Following are the values of a function y(x) : y(-1) = 5, y(0), y(1)    as per Newton’s central  difference scheme is: 

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Test: Theorems of Integral Calculus- 2 - Question 3

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the squeeze theorem for this. Recall that sinx is only defined on −1≤sinx≤1. Therefore

Test: Theorems of Integral Calculus- 2 - Question 4

The function f(x) = |x+1| on the interval [-2, 0] 

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f(x ) = x+ 1

f is continuous in [−2, 0]

but not differentiable at

x =−1 because we can draw

infinite number of tangents at x = −1

Test: Theorems of Integral Calculus- 2 - Question 5

If y=|x| for x<0 and y=x for x ≥ 0, then 

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Test: Theorems of Integral Calculus- 2 - Question 6

What is the derivative of f(x) = |x| at x = 0? 

Detailed Solution for Test: Theorems of Integral Calculus- 2 - Question 6

f( x ) = x .

At x = 0, we can draw infinitely many tangents at x=0.So limit does not exists. 

 

Test: Theorems of Integral Calculus- 2 - Question 7

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= 1.0= 1

Test: Theorems of Integral Calculus- 2 - Question 8

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Test: Theorems of Integral Calculus- 2 - Question 9

The function Y=| 2-3x |  

Test: Theorems of Integral Calculus- 2 - Question 10

Test: Theorems of Integral Calculus- 2 - Question 11

The function f(x) = x3 - 6x2 + 9x + 25 has

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Test: Theorems of Integral Calculus- 2 - Question 12

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Test: Theorems of Integral Calculus- 2 - Question 13

The value of the integral   is

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Test: Theorems of Integral Calculus- 2 - Question 14

The following plot shows a function y which varies linearly with x. The value of the integral I = 

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Here the points (0,1) and (-1,0) are on the time

∴The equn of the line is

Test: Theorems of Integral Calculus- 2 - Question 15

The value of the integral 

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Test: Theorems of Integral Calculus- 2 - Question 16

The length of the curve    between x = 0 and x = 1 is 

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Length of  the wire 

Test: Theorems of Integral Calculus- 2 - Question 17

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Test: Theorems of Integral Calculus- 2 - Question 18

A continuous-time system is described by y (t) = e − x (t) where y (t) is the output and x (t) is the input. y(t) is bounded. 

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Test: Theorems of Integral Calculus- 2 - Question 19

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Since

Test: Theorems of Integral Calculus- 2 - Question 20

The value of the quantity P, where 

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