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

*According to the latest update on the term-wise CBSE Syllabus 2021-22, Limits is included in the term – I and Derivatives is included in the term – II.

The best way to boost the confidence of the students is to practise as many questions as possible. To practise more questions, there is no better resource than the NCERT textbook. Chapter 13 Limits and Derivatives of Class 11 Maths is categorized partly under both the term – I and II CBSE Syllabus for the 2021-22 session. Here is a glance of what the first exercise of Chapter 13 in Class 11 Maths is all about. Exercise 13.1 of NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives are based on the following topics:

  1. Introduction to Limits And Derivatives
  2. Intuitive Idea of Derivatives
  3. Limits
    1. Algebra of limits
    2. Limits of polynomials and rational functions
  4. Limits of Trigonometric Functions

Downloading and practising the NCERT Solutions of Class 11 Maths will help the students in understanding the concepts covered in Class 11 well. Once the students attain a good knowledge of the concepts, they would be able to perform effectively in the term – I and II examinations.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives Exercise 13.1

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Access Other Exercises for Class 11 Maths Chapter 13

Exercise 13.2 Solutions 11 Questions

Miscellaneous Exercise On Chapter 13 Solutions 30 Questions

Access Solutions for Class 11 Maths Chapter 13.1 Exercise

1. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 1

Solution:

Given

NCERT Solutions Mathematics Class 11 Chapter 13 - 2

Substituting x = 3, we get

= 3 + 3

= 6

2. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 3

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 4

Substituting x = π, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 5= (π – 22 / 7)

3. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 6

Solution:

Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 7

Substituting r = 1, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 8= π(1)2

= π

4. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 9

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 10

Substituting x = 4, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 11= [4(4) + 3] / (4 – 2)

= (16 + 3) / 2

= 19 / 2

5. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 12

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 13

Substituting x = -1, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 14

= [(-1)10 + (-1)5 + 1] / (-1 – 1)

= (1 – 1 + 1) / – 2

= – 1 / 2

6. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 15

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 16

= [(0 + 1)5 – 1] / 0

=0

Since, this limit is undefined

Substitute x + 1 = y, then x = y – 1

NCERT Solutions Mathematics Class 11 Chapter 13 - 17

7. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 18

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 19

8. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 20

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 21

9. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 22

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 23

= [a (0) + b] / c (0) + 1

= b / 1

= b

10. Evaluate the Given limit: NCERT Solutions Mathematics Class 11 Chapter 13 - 24

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 25

11. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 26

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 27

Substituting x = 1

NCERT Solutions Mathematics Class 11 Chapter 13 - 28

= [a (1)2 + b (1) + c] / [c (1)2 + b (1) + a]

= (a + b + c) / (a + b + c)

Given

NCERT Solutions Mathematics Class 11 Chapter 13 - 29

= 1

12. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 30

Solution:

By substituting x = – 2, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 31

13. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 32

Solution:

Given NCERT Solutions Mathematics Class 11 Chapter 13 - 33

NCERT Solutions Mathematics Class 11 Chapter 13 - 34

14. Evaluate the given limit: NCERT Solutions Mathematics Class 11 Chapter 13 - 35

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 36

15. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 37

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 38

16. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 39

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 40

17. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 41

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 42

NCERT Solutions Mathematics Class 11 Chapter 13 - 43

18. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 44

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 45

19. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 46

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 47

20. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 48

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 49

NCERT Solutions Mathematics Class 11 Chapter 13 - 50

21. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 51

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 52

NCERT Solutions Mathematics Class 11 Chapter 13 - 53

22. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 54

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 55

NCERT Solutions Mathematics Class 11 Chapter 13 - 56

23.
NCERT Solutions Mathematics Class 11 Chapter 13 - 57

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 58

NCERT Solutions Mathematics Class 11 Chapter 13 - 59

NCERT Solutions Mathematics Class 11 Chapter 13 - 60

24. Find
NCERT Solutions Mathematics Class 11 Chapter 13 - 61, where

NCERT Solutions Mathematics Class 11 Chapter 13 - 62

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 63

NCERT Solutions Mathematics Class 11 Chapter 13 - 64

25. Evaluate
NCERT Solutions Mathematics Class 11 Chapter 13 - 65, where f(x) =
NCERT Solutions Mathematics Class 11 Chapter 13 - 66

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 67

NCERT Solutions Mathematics Class 11 Chapter 13 - 68

NCERT Solutions Mathematics Class 11 Chapter 13 - 69

26. Find
NCERT Solutions Mathematics Class 11 Chapter 13 - 70, where f (x) =
NCERT Solutions Mathematics Class 11 Chapter 13 - 71

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 72

NCERT Solutions Mathematics Class 11 Chapter 13 - 73

27. Find
NCERT Solutions Mathematics Class 11 Chapter 13 - 74, where
NCERT Solutions Mathematics Class 11 Chapter 13 - 75

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 76

NCERT Solutions Mathematics Class 11 Chapter 13 - 77

28. Suppose
NCERT Solutions Mathematics Class 11 Chapter 13 - 78and if
NCERT Solutions Mathematics Class 11 Chapter 13 - 79what are possible values of a and b

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 80

NCERT Solutions Mathematics Class 11 Chapter 13 - 81

29. Let a1, a2,………an be fixed real numbers and define a function

f (x) = (x – a1) (x – a2) ……. (x – an).

What is
NCERT Solutions Mathematics Class 11 Chapter 13 - 82For some a ≠ a1, a2, ……. an, compute
NCERT Solutions Mathematics Class 11 Chapter 13 - 83

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 84

NCERT Solutions Mathematics Class 11 Chapter 13 - 85

30. If NCERT Solutions Mathematics Class 11 Chapter 13 - 86 For what value (s) of a does NCERT Solutions Mathematics Class 11 Chapter 13 - 87exists?

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 88

NCERT Solutions Mathematics Class 11 Chapter 13 - 89

NCERT Solutions Mathematics Class 11 Chapter 13 - 90

NCERT Solutions Mathematics Class 11 Chapter 13 - 91

31. If the function f(x) satisfies NCERT Solutions Mathematics Class 11 Chapter 13 - 92, evaluateNCERT Solutions Mathematics Class 11 Chapter 13 - 93

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 94

NCERT Solutions Mathematics Class 11 Chapter 13 - 95

32. If NCERT Solutions Mathematics Class 11 Chapter 13 - 96 For what integers m and n does both NCERT Solutions Mathematics Class 11 Chapter 13 - 97and NCERT Solutions Mathematics Class 11 Chapter 13 - 98exist?

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 99

NCERT Solutions Mathematics Class 11 Chapter 13 - 100

NCERT Solutions Mathematics Class 11 Chapter 13 - 101

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