Continuity and Differentiability - 1 - Free MCQ Test with solutions

if f(x) is not continuous at x = a, then it is not differentiable at x = a.

If f(x) is continuous at x = a, then it is differentiable at x = a.

if f(x) and g(x) are differentiable at x = a. then f(x) + g(x) is also differentiable at x = a.

{–1, 1}

{–1, 0}

{0, 1}

{–1, 0, 1}

p

p – 1

2p + 1

2p – 1

3

4

5

6

2/3

3/2

3

1

4

5

3

2

2

3

4

5

f'(1) = f'(0) + 1

f'(1) = f'(0) – 1

f'(0) = f'(1) + 2

f'(0) = f'(1) – 2

ƒ is continuous and derivable at x = 0

ƒ is continuous but not derivable at x = 0

ƒ may be discontinuous at x = 0

None of these

equal to 0

equal to 1

ln π/2

non existent

continuous every where

continuous no where

continuous at x = 0

continuous only at x = 0

all integers

all integers except 0 and 1

all integers except 0

all integers except 1

a = 2/3, b = e²

a =1/3, b = e^1/3

a = 2/3, b = e^2/3

None of these

All x

All integer points

No x

x which is not an integer

every where continuous

discontinuous at all integer values of x

continuous at x = 0

None of these

1/16

1/32

– 1/64

1/128

continuous everywhere

continuous nowhere

discontinuous at x = 0

none of these

π/5

5/π

1

0