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NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2.

  • Limits and Derivatives Class 11 Ex 13.1
Board CBSE
Textbook NCERT
Class Class 11
Subject Maths
Chapter Chapter 13
Chapter Name Limits and Derivatives
Exercise Ex 13.2
Number of Questions Solved 11
Category NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2

Ex 13.2 Class 11 Maths Question 1.
Find the derivative of x2 – 2 at x = 10.
Solution:
let f(x) = x2 – 2
Differentiating (i) with respect to x, we get
f'(x) = 2x
At x = 10, f'(10) = 2(10) = 20.

Ex 13.2 Class 11 Maths Question 2.
Find the derivative of 99x at x = 10.
Solution:
let f(x) = 99x
Differentiating (i) with respect to x, we get
f'(x) = 90
At x = 100, f'(100) = 99.

Ex 13.2 Class 11 Maths Question 3.
Find the derivative of x at x = 10.
Solution:
let f(x) = x
Differentiating (i) with respect to x, we get
f'(x) = 1
At x = 1, f'(1) = 1.

Ex 13.2 Class 11 Maths Question 4.
Find the derivative of the following functions from first principle.
(i) x3 – 27
(ii) (x – 1)(x – 2)
(iii) \(\frac { 1 }{ { x }^{ 2 } } \)
(iv) \(\frac { x+1 }{ x-1 } \)
Solution:
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 1
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 3
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 4
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 5

Ex 13.2 Class 11 Maths Question 5.
For the function
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 6
Prove that f'(1) = 100f'(0)
Solution:
We have
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 7

Ex 13.2 Class 11 Maths Question 6.
Find the derivative of xn + axn-1 + a2xn-2+
…. + an-1x + an for some fixed real number a.
Solution:
Let f(x) = xn + axn-1 + a2xn-2+
…. + an-1x + an
Differentiating (i) with respect to x, we get
f'(x) = nxn-1 + (n – 1)axn-2 + …… + an-1

Ex 13.2 Class 11 Maths Question 7.
For some constants a and b, find the derivative of
(i) (x – a)(x – b)
(ii) (ax2 + b)2
(iii) \(\frac { x-a }{ x-b } \)
Solution:
(i) Let f(x) = (x – a)(x – b) ….(1)
Differentiating (1) with respect to x, we get
f'(x) = (x – a)(x – b)’ + (x – a)’ (x – b)
⇒ f'(x) = (x – a) + (x – b) = 2x – a – b
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 8

Ex 13.2 Class 11 Maths Question 8.
Find the derivative \(\frac { { x }^{ n }-{ a }^{ n } }{ x-a } \) for some constant a.
Solution:
Let f(x) = \(\frac { { x }^{ n }-{ a }^{ n } }{ x-a } \) ….(i), where a is a constant.
Differentiating (i) with respect to x, we get
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 9

Ex 13.2 Class 11 Maths Question 9.
Find the derivative of
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 10
Solution:
(i) Let f(x) = \(2x-\frac { 3 }{ 4 } \) …(1)
Differentiating (i) with respect to x, we get
f'(x) = 2·1 – 0 ⇒ f'(x) = 2.
(ii) Let f(x) = 5x3 + 3x – 1)(x – 1)
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 11
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 12
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 13

Ex 13.2 Class 11 Maths Question 10.
Find the derivative of cos x from first principle.
Solution:
Let f(x) = cos x
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 14
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 15

Ex 13.2 Class 11 Maths Question 11.
Find the derivative of the following functions:
(i) sin x cos x
(ii) secx
(iii) 5 secx + 4 cosx
(iv) cosecx
(v) 3 cotx + 5 cosecx
(vi) 5sinx – 6 cosx + 7
(vii) 2 tanx – 7 secx.
Solution:
(i) Let f(x) = sin x cos x … (1)
Differentiating (1) with respect to x, we get
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 16
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 17
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 18

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