MP Board Class 11th Maths Important Questions Chapter 13 Limits and Derivatives

MP Board Class 11th Maths Important Questions Chapter 13 Limits and Derivatives

MP Board Class 11th Maths Important Questions Chapter 13 Limits and Derivatives

Limits and Derivatives Short Answer Type Questions

Evaluate the following limits :

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.
If  = 405, then find the value of n.
Solution:

Question 10.
Find the value of :

Solution:

Question 11.

Solution:

Question 12.

Question 13.

Question 14.
Differentiate sin(x + a) w.r.t. x.
Solution:
Let y = sin(x + a)
y = sin x cos a + cos x sin a

Question 15.
Differentiate cosecx.cotx w.r.t. x.
Solution:
Let y = cosec x. cot x

Question 16.

Question 17.

Question 18.
Differentiate sinⁿ x w.r.t. x.
Solution:
Let y = sinⁿ x

Limits and Derivatives Long Answer Type Questions

Question 1.
Let f(x) =
, then find the value of a and b.
Solution:

Question 2.
Find the value of , where

Solution:

Question 3.
f(x) is defined such that
 and  is exist x = 2, then find the value of k.
Solution:

Question 4.
If the function f(x) satisfies= π, then find the value of 
Solution:

Question 5.
Find the differential coefficient of the following functions by using first principle method :
(i) sin(x + 1), (ii) cos(x – π/8,
Solution:
(i) Let f(x) = sin(x + 1)
∴ f(x + h) = sin[x + h + 1]
By definition of first principle,

By definition of first principle,

Find the differential coefficient of the following functions

Question 6.
(ax² + sin x)(p + q cos x). (NCERT)
Solution:
Let y = (ax² + sin x)(p + q cos x).

Question 7.
(x + cos x)(x – tan x) (NCERT)
Solution:
Let y = (x + cos x)(x – tan x)

Question 8.

Question 9.

Question 10.

Question 11.

Question 12.

Question 13.

Question 14.

Question 15.

f'(1) = 100 f'(0). (NCERT)
Solution:
Put x = 1, we get
f'(1) = 1 + 1 + ………. 1 + 1 (100 times)
f’(1) = 100 …. (1)
Put x = 0, we get
f'(0) = 0 + 0 + ……… 0 + 1
f’(0) = 1 …. (2)
From equation (1) and (2),
f'(1) = 100 f'(0).

Question 16.
Find the differential coefficient of cos x by first principle method. (NCERT)
Solution:
Let f(x) = cosx
∴ f(x + h) = cos(x + h)
By definition of first principle

Question 17.