RD Sharma Solutions for Class 11 Chapter 29 - Limits

This chapter mainly deals with problems based on limits and how it is derived. For students who find Maths to be a difficult subject, experts have explained the topics step by step to make learning Maths fun and to help them understand the concepts easily. Solved examples are available before the exercise wise problems for students to practice the problems. The solutions pdf mainly contain answers with explanations in an interactive manner to help students perform well in the board exam. To get a clear idea about the method of solving problems, students can use RD Sharma Class 11 Maths Solutions pdf, from the links given below.

Chapter 29 – Limits contains eleven exercises and the RD Sharma Solutions present in this page provide solutions to the questions present in each exercise. Now, let us have a look at the concepts discussed in this chapter.

  • Informal approach to limit.
  • Evaluation of left hand and right hand limits.
  • Difference between the value of a function at a point and the limit at that point.
  • The algebra of limits.
  • Indeterminate forms and evaluation of limits.
  • Evaluation of algebraic limits.
    • Direct substitution method.
    • Factorization method.
    • Rationalisation method.
    • Evaluation of algebraic limits by using some standard limits.
    • Method of evaluation of algebraic limits at infinity.
  • Evaluation of trigonometric limits.
    • Evaluation of trigonometric limits when the variable tends to zero.
    • Evaluation of trigonometric limits when variables tend to a non-zero quantity.
    • Evaluation of trigonometric limits by factorisation.
  • Evaluation of exponential and logarithmic limits.

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EXERCISE 29.1 PAGE NO: 29.11

1. Show that RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 1 does not exist.

Solution:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 2

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 3

Solution:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 4

So, let x = 2 – h, where h = 0

Substituting the value of x, we get

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 5

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 6

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 7

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 8

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 9

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 10


EXERCISE 29.2 PAGE NO: 29.18

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 11

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 12

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 13

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 14

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 15

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 16


EXERCISE 29.3 PAGE NO: 29.23

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 17

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 18

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 19

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 20

∴ The value of the given limit is ½.

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 21

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 22

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 23

By substituting the value of x, we get

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 24

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 25

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 26


EXERCISE 29.4 PAGE NO: 29.28

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 27

∴ The value of the given limit is ½.

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 28

We need to find the limit of the given equation when x => 0

Now let us substitute the value of x as 0, we get an indeterminate form of 0/0. 

Let us rationalizing the given equation, we get

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 29

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 30

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 31

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 32

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 33

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 34

∴ The value of the given limit is ½.


EXERCISE 29.5 PAGE NO: 29.33

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 35

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 36

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 37

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 38

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 39

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RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 43

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 44

EXERCISE 29.6 PAGE NO: 29.38

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 45

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 46

= 3 / 2

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 47

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 48

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 49

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 50

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 51


EXERCISE 29.7 PAGE NO: 29.49

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 52

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 53

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 54

So,

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 55

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 56

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 57

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 58

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 59

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 60


EXERCISE 29.8 PAGE NO: 29.62

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 61

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 62

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 63

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 64

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 65

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 66

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 67

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 68

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 69


EXERCISE 29.9 PAGE NO: 29.65

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 70

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 71

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 72

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 73

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 74

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 75

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 76

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 77

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 78

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 79

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 80


EXERCISE 29.10 PAGE NO: 29.71

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 81

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 82

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 83

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 84

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 85

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 86

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 87


EXERCISE 29.11 PAGE NO: 29.71

Evaluate the following limits:

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 88

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 89

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 90

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 91

So here,

f (x) = cos x + sin x – 1

g (x) = x

Then,

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 92

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 93

RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits - image 94

Also, access exercises of RD Sharma Solutions for Class 11 Maths Chapter 29 – Limits

Exercise 29.1 Solutions

Exercise 29.2 Solutions

Exercise 29.3 Solutions

Exercise 29.4 Solutions

Exercise 29.5 Solutions

Exercise 29.6 Solutions

Exercise 29.7 Solutions

Exercise 29.8 Solutions

Exercise 29.9 Solutions

Exercise 29.10 Solutions

Exercise 29.11 Solutions

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