Test: Theorems of Integral Calculus- 1
20 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | Test: Theorems of Integral Calculus- 1
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As x is increased from – ∞ to ∞ , the function
Given
Square both side, we get
cos x and sin x are finite whatever x may be
Which of the following functions is not differentiable in the domain [-1,1]?
then limx-►3 f(x) will be 
= 1/12
What should be the value of λ such that the function defined below is continuous at x = π/2?
By the given condition
From (1), λ = 1
Consider the function f(x) = |x|3, where x is real. Then the function f(x) at x = 0 is
The expression e–ln x for x > 0 is equal to
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?
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.
is given by
Which one of the following function is strictly bounded?
For a strictly bounded function f(x), limit should be finite
Which of the following integrals is unbounded?
What is the value of the definite integral, 
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