## Kerala Plus One Maths Chapter Wise Questions and Answers Chapter 13 Limits and Derivatives

**Short Answer** **Type Questions **

**(Score 3)**

Question 1.

a. Let ,then left hand limit

a. 0

b.

1/2

c. -1/2

d. Does not exist

b.

If

then find the positive value of K

Answer:

a. Does not exist

Question 2.

a. If x is the radian

a. 0

b. 1

c. -1

d. 2

b. Prove that

Answer:

a.1

b.

Question 3.

Answer:

Question 4.

a. Let f(x) =2x^{2}+3x=5,then f’(0)+3f’(-1) =…………..

a. 0

b. 1

c. -1

d.2

b. Find

Answer:

a. 0

f(x) = 2x^{2}+3x-5

f'(x) = 4x + 3,f'(0) = 3

Question 5.

Answer:

ii. 2k=7 or k=2k

Question 6.

Answer:

Question 7.

a. Find the derivative of f(x) = ax+ b, where a and b are non-zero constants, by first principle.

b. Compute the derivative of f(x) = sin^{2}x.

Answer:

a. We have, f(x) = ax+b

By definition of first principle, we have

Question 8.

a. Evaluate

a. 1

b. 0

c. -1

d. 1/e

Answer:

**Short Answer** **Type Questions **

**(Score 4)**

Question 1.

Differentiate the following with respect to x

i.

ii. (ax^{2}+sinx)(p +qcosx)

Answer:

Question 2.

Evaluate

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

a. Differentiate (x + sec x) (x – tan x)

b. Show that the following limit does not exits

c. Differentiate using quotient rule.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Evaluate

Answer:

Question 9.

a. 0

b. 1

c. 2

d. 1/3

Answer:

c. 2

Dividing numerator and denominator by z-1

**Long Answer** **Type Questions **

**(Score 6)**

Question 1.

Evaluate the following Limits

Answer:

Question 2.

i. Express (sin x-sin x) as a product

Answer:

Question 3.

a. Find the derivative of sinx+cosx from first principle.

B. Find the derivative of sin (x + 1) from first principle.

Answer:

Question 4.

Match the following:

Answer:

Question 5.

Answer:

Question 6.

a. choose the correct value of

from the bracket.(1/2,-1/2,1/3,0)

b.

c.

Answer:

Question 7.

a. Find the derivative of from first principle

b. Find the derivative of (ax +b)^{n} (ax+c)^{m }Answer:

Question 8.

Choose the most appropriate answer from those given in the bracket.

Choose either (a), (b), (c) or (d), (e), (f)

Answer:

Question 9.

Choose the most appropriate answer from those given in the bracket.

Choose either (a), (b), (c) or (d), (e), (f)

Answer: