CBSE Class 11 Maths Limits and Derivatives Quiz 2

1.

The value of Lim_n→∞ {1² + 2² + 3² + …… + n²}/n³ is

A

0

B

1

C

-1

D

n

2.

The value of Lim_n→∞ (sin x/x) is

A

0

B

1

C

-1

D

None of these

3.

The value of Lim_x→0 ax is

A

0

B

1

C

1/2

D

3/2

4.

Let f(x) = cos x, when x ≥ 0 and f(x) = x + k, when x < 0 Find the value of k given that Lim_x→0 f(x) exists.

A

0

B

1

C

-1

D

None of these

5.

The value of Lim_x→0 (1/x) × sin^-1 {2x/(1 + x²) is

A

0

B

1

C

2

D

-2

6.

Lim_x→0 sin (ax)/bx is

A

0

B

1

C

a/b

D

b/a

7.

The value of the limit Lim_x→0 {log(1 + ax)}/x is

A

0

B

1

C

a

D

1/a

8.

If f(x) = (x + 1)/x then df(x)/dx is

A

1/x

B

-1/x

C

-1/x²

D

1/x²

9.

Lim_x→0 (e^x² – cos x)/x² is equals to

A

0

B

1

C

2/3

D

3/2