NCERT Solutions Class 11th Maths Chapter 13 – Limits And Derivatives Exercise 13.1

June 13, 2022

NCERT Solutions Class 11th Maths Chapter 13 – Limits And Derivatives Exercise 13.1

Textbook	NCERT
class	Class – 11th
Subject	Mathematics
Chapter	Chapter – 13
Chapter Name	Limits And Derivatives
grade	Class 11th Maths solution
Medium	English
Source	last doubt

NCERT Solutions Class 11th Maths Chapter 13 – Limits And Derivatives Exercise 13.1

?Chapter – 13?

✍Limits And Derivatives✍

?Exercise 13.1?

1. Evaluate the Given limit:

Solution: Given

Substituting x = 3, we get
= 3 + 3
= 6

2. Evaluate the Given limit:

Solution: Given limit:

Substituting x = π, we get

= (π – 22 / 7)

3. Evaluate the Given limit:

Solution: Given limit:

Substituting r = 1, we get

= π(1)2
= π

4. Evaluate the Given limit:

Solution: Given limit:

Substituting x = 4, we get

= [4(4) + 3] / (4 – 2)
= (16 + 3) / 2
= 19 / 2

5. Evaluate the Given limit:

Solution: Given limit:

Substituting x = -1, we get

= [(-1)10 + (-1)5 + 1] / (-1 – 1)
= (1 – 1 + 1) / – 2
= – 1 / 2

6. Evaluate the Given limit:

Solution: Given limit:

= [(0 + 1)⁵ – 1] / 0
=0
Since, this limit is undefined
Substitute x + 1 = y, then x = y – 1

7. Evaluate the Given limit:

Solution:

8. Evaluate the Given limit:

Solution:

9. Evaluate the Given limit:

Solution:

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

10. Evaluate the Given limit:

Solution:

11. Evaluate the Given limit:

Solution: Given limit:

Substituting x = 1

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

12. Evaluate the Given limit:

Solution: By substituting x = – 2, we get

13. Evaluate the Given limit:

Solution: Given

14. Evaluate the given limit:

Solution:

15. Evaluate the given limit:

Solution:

16. Evaluate the given limit:

Solution:

17. Evaluate the given limit:

Solution:

18. Evaluate the given limit:

Solution:

19. Evaluate the given limit:

Solution:

20. Evaluate the given limit:

Solution:

21. Evaluate the given limit:

Solution:

22. Evaluate the given limit:

Solution:

23.

Solution:

24. Find

, where

Solution:

25. Evaluate

, where f(x) =

Solution:

26. Find

, where f (x) =

Solution:

27. Find

, where

Solution:

28. Suppose

and if

what are possible values of a and b

Solution:

29. Let a₁, a_2,………a_n be fixed real numbers and define a function

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

What is

For some a ≠ a₁, a₂, ……. a_n, compute

Solution:

30. If

For what value (s) of a does

exists?

Solution:

31. If the function f(x) satisfies

, evaluate

Solution:

32. If

For what integers m and n does both

and

exist?

Solution: