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Chapter 13 Limits and Derivatives Ex 13.1 Solutions

Question - 1 : - Evaluate the Given limit: 

Answer - 1 : -

Given

Substituting x = 3, we get

= 3 + 3

= 6

Question - 2 : - Evaluate the Given limit: 

Answer - 2 : -

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

Question - 3 : - Evaluate the Given limit: 

Answer - 3 : -

Given limit: 
Substituting r = 1, we get
 
= π(1)2
= π

Question - 4 : - Evaluate the Given limit: 

Answer - 4 : -

Given limit:
 
Substituting x = 4, we get
 = [4(4) + 3] / (4 – 2)
= (16 + 3) / 2
= 19 / 2

Question - 5 : - Evaluate the Given limit: 

Answer - 5 : -

Given limit:
 
Substituting x = -1, we get
 
= [(-1)10 + (-1)5 + 1] / (-1 – 1)
= (1 – 1 + 1) / – 2
= – 1 / 2

Question - 6 : - Evaluate the Given limit: 

Answer - 6 : -

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

Question - 7 : - Evaluate the Given limit: 

Answer - 7 : -


Question - 8 : - Evaluate the Given limit: 

Answer - 8 : -


Question - 9 : - Evaluate the Given limit: 

Answer - 9 : -

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

= b / 1

= b

Question - 10 : - Evaluate the Given limit:  

Answer - 10 : -


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