Limits, Continuity and Differentiability Test

Result

Limits, Continuity and Differentiability Test - 35

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Rank
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Weekly Quiz Competition

Question 1
4 / -1

If f is a continuous function such that f(0) = f(1) = 0, f '(1) = 2 and y(x) = f(e^x) e^f(x) then y'(0) is

A
0

B
1

C
2

D
none of these

Solution
Question 2
4 / -1

A

B
b

C
b²

D
none of these

Solution
Question 3
4 / -1

A
e^–1

B
e^–2

C
e

D
e²

Solution
Question 4
4 / -1

The function f(x) = sin|x| is

A
Continuous for all x

B
Continuous only at certain points

C
Differentiable at all points

D
None of the above

Solution
Question 5
4 / -1

If f(x) = |x|, then f(x) is

A
Continuous for all x

B
Differentiable at x = 0

C
Neither continuous nor differentiable at x = 0

D
None of the above

Solution
Question 6
4 / -1

A
f(x) is discontinuous everywhere

B
f(x) is continuous everywhere

C
f' (x) exists in (–1, 1)

D
f' (x) exists in (–2,2)

Solution
Question 7
4 / -1

At the point x = 1, the given function

A
Continuous and differentiable

B
Continuous and not differentiable

C
Discontinuous and differentiable

D
Discontinuous and not differentiable

Solution
Question 8
4 / -1

Let [x] denotes the greatest integer less than or equal to x. If f(x) = [x sin πx], then f(x) is

A
Continuous at x = 0

B
Continuous in (–1, 0)

C
Differentiable in (–1, 1)

D
All of the above

Solution
Question 9
4 / -1

A
Is continuous but not differentiable

B
Is discontinuous

C
Is having continuous derivative

D
Is continuous and differentiable

Solution
Question 10
4 / -1

A
0

B
1

C
2

D
3

Solution