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

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

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

NCERT Solutions for Class 11 Maths Chapter-13 Limits and Derivatives Exercise 13.1 is prepared by the expert of Physics Wallah score more with Physics Wallah NCERT Class 11 maths solutions. You can download and share NCERT Solutions for Class 11 Maths.

NCERT Solutions for Class-11 Maths Exercise 13.1

Evaluate the following limits in Exercises 1 to 22.

Question 1.

Solution :

Given that,

Substituting x = 3, we get

= 3 + 3 = 6

Question 2.

Solution :

Given that,

Substituting x = π, we get
=(π – 22 / 7)

Question 3.

Solution :

Given that,

Substituting r = 1, we get
= π(1) ² = π

Question 4.

Solution :
given limit,

Substituting x = 4, we get

= [4(4) + 3] / (4 – 2) =

= (16 + 3) / 2

= 19 / 2

Question 5.

Solution :

Given that,

Substituting x = -1, we get

= [(-1) ¹⁰ + (-1) ⁵ + 1] / (-1 – 1)

= (1 – 1 + 1) / – 2

= – 1 / 2

Question 6.

Solution :
Given limit,

Putting x as 0

= [(0 + 1) ⁵ – 1] / 0

=0

Since, this limit is undefined

Substitute x + 1 = y, then x = y – 1

=5

Question 7.

Solution :

Question 8.

Solution :

Question 9.

Solution :
Given that,

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

= b / 1

= b

Question 10.

Solution :

Question 11.

Solution :
Given that,

Substituting x = 1

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

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

= 1

Question 12.

Solution :

Question 13.

Solution :
Given that

Question 14.

Solution :

Question 15.

Solution :

Question 16.

Solution :

Question 17.

Solution :

Question 18.

Solution :

Question 19.

Solution :

Question 20.

Solution :

Question 21.

Solution :

Question 22.

Solution :

= 1 x 2

= 2

Question 23. Find and where

Solution :

Question 24. Find where

Solution :
Given:

.

Question 25. Evaluate where

Solution :
Given:

.

Question 26. Find Where

Solution :
Given:

Question 27. Find where

Solution :
Given:

Question 28. Suppose and if what are possible values of a and b?

Solution :
Given: and

Question 29. Let a ₁ , a _2, ………a _n be fixed real numbers and define a function f (x) = (x – a ₁ ) (x – a ₂ ) ……. (x – a _n ). What is For some a ≠ a ₁ , a ₂ , ……. a _n , compute

Solution :

Question 30. If for what values of (s) does exists?

Solution :

Question 31. If the function f(x) satisfies valuate

Solution :

Question 32. If for what integer m and n does both and exist?

Solution :
Given function is