NCERT Solutions | Class 11 Maths Chapter 13

NCERT Solutions | Class 11 Maths Chapter 13 | Limits and derivatives 

NCERT Solutions for Class 11 Maths Chapter 13 Limits and derivatives

CBSE Solutions | Maths Class 11

Check the below NCERT Solutions for Class 11 Maths Chapter 13 Limits and derivatives Pdf free download. NCERT Solutions Class 11 Maths  were prepared based on the latest exam pattern. We have Provided Limits and derivatives Class 11 Maths NCERT Solutions to help students understand the concept very well.

NCERT | Class 11 Maths

NCERT Solutions Class 11 Maths
Book: National Council of Educational Research and Training (NCERT)
Board: Central Board of Secondary Education (CBSE)
Class: 11th
Subject: Maths
Chapter: 13
Chapters Name: Limits and derivatives
Medium: English

Limits and derivatives | Class 11 Maths | NCERT Books Solutions

You can refer to MCQ Questions for Class 11 Maths Chapter 13 Limits and derivatives to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1

Evaluate the following limits in Exercises 1 to 22.

Ex 13.1 Class 11 Maths Question 1.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 1
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 2

Ex 13.1 Class 11 Maths Question 2.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 3
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 4

Ex 13.1 Class 11 Maths Question 3.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 5
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 6

Ex 13.1 Class 11 Maths Question 4.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 7
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 8

Ex 13.1 Class 11 Maths Question 5.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 9
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 10

Ex 13.1 Class 11 Maths Question 6.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 11
Solution.

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 12
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 13

Ex 13.1 Class 11 Maths Question 7.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 14
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 15

Ex 13.1 Class 11 Maths Question 8.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 16
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 17

Ex 13.1 Class 11 Maths Question 9.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 18
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 19

Ex 13.1 Class 11 Maths Question 10.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 20
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 21

Ex 13.1 Class 11 Maths Question 11.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 22
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 23

Ex 13.1 Class 11 Maths Question 12.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 24
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 25

Ex 13.1 Class 11 Maths Question 13.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 26
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 27
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 28

Ex 13.1 Class 11 Maths Question 14.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 29
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 30

Ex 13.1 Class 11 Maths Question 15.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 31
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 32

Ex 13.1 Class 11 Maths Question 16.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 33
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 34

Ex 13.1 Class 11 Maths Question 17.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 35
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 36
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 37

Ex 13.1 Class 11 Maths Question 18.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 38
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 39

Ex 13.1 Class 11 Maths Question 19.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 40
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 41

Ex 13.1 Class 11 Maths Question 20.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 42
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 43

Ex 13.1 Class 11 Maths Question 21.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 44
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 45

Ex 13.1 Class 11 Maths Question 22.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 46
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 47

Ex 13.1 Class 11 Maths Question 23.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 48
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 49

Ex 13.1 Class 11 Maths Question 24.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 50
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 51

Ex 13.1 Class 11 Maths Question 25.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 52
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 53

Ex 13.1 Class 11 Maths Question 26.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 54
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 55
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 56

Ex 13.1 Class 11 Maths Question 27.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 57
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 58

Ex 13.1 Class 11 Maths Question 28.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 59
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 60
Adding (ii) and (iii), we get 2b = 8 ⇒ b = 4
Subtituting the value of b in (iii), we get
4 – a = 4 ⇒ a = 0
Thus a = 0 and b = 4.

Ex 13.1 Class 11 Maths Question 29.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 61
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 62

Ex 13.1 Class 11 Maths Question 30.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 63
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 64
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 65

Ex 13.1 Class 11 Maths Question 31.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 66
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 67

Ex 13.1 Class 11 Maths Question 32.


NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 68
Solution.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 69

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 x22 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
NCERT Class 11 Maths

Class 11 Maths Chapters | Maths Class 11 Chapter 13

Chapterwise NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 12 All Subjects NCERT Solutions for Class 10 All Subjects
NCERT Solutions for Class 11 All Subjects NCERT Solutions for Class 9 All Subjects

NCERT SOLUTIONS

Post a Comment

इस पेज / वेबसाइट की त्रुटियों / गलतियों को यहाँ दर्ज कीजिये
(Errors/mistakes on this page/website enter here)

Previous Post Next Post