Limits, Continuity and Differentiability Test

Result

Limits, Continuity and Differentiability Test - 87

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Weekly Quiz Competition

Question 1
4 / -1

A
1

B
–1

C
∞

D
Does not exist

Solution
Question 2
4 / -1

The function which is continuous for all real values of x and differentiable at x = 0 is

A
|x|

B
log x

C
sin x

D
x^1/2

Solution
Question 3
4 / -1

A
1

B
–1

C
0

D
Does not exist

Solution
Question 4
4 / -1

A
f is differentiable at x = 0 and at x = 1

B
f is differentiable at x = 0 but not at x = 1

C
f is differentiable at x = 1 but not at x = 0

D
f is neither differentiable at x = 0 nor at x = 1

Solution
Question 5
4 / -1

A
f(x) is continuous but non-differentiable at x = 0

B
f(x) is differentiable at x = 0

C
f(x) is not differentiable at x = 0

D
None of the above
Question 6
4 / -1

The differentiable function f,g,h are such that f\' (x) = g(x), g\'(x) = h(x), h\'(x) = f(x), f(0) = 1,g(0) = 0 and h(0) = 0.Then the value of f³ (x) + g³ (x) + h³ (x) – 3f(x)g(x)h(x) at x = 5 is

A
0

B
1

C
2

D
3

Solution
Question 7
4 / -1

A differentiable function f(x) is defined for all x > 0 and satisfies f(x³) = 4x⁴ for all x > 0.The value of f\' (8) is

A

B

C

D

Solution
Question 8
4 / -1

The period of the function f(x) = |sin x| + |cos x| is

A
2π

B
3π

C

D
Question 9
4 / -1

A
f(x) is continuous but not differentiable at x = 0

B
f(x) is not differentiable at x = 0

C
f(x) is differentiable at x = 0

D
None of the above

Solution
Question 10
4 / -1

A

B

C

D

Solution