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

EXERCISE 13.1 Evaluate the following limits in Exercises 1 to 22

Question 1:3 lim 3 x x  +

Question 2: 22 lim x 7 x   −  
 

NCERT class 11 maths chapter 13 Limits and Derivatives

Question 3:2 1 lim r r 

Question 4:4 4 3 lim x 2 x  x + −

Question 5:10 5 1 1 lim x 1 x x  − x + + −

Exercise 13.1 maths class 11 Chapter 13 Limits and Derivatives

Question 6:( )5 0 1 1 lim x x  x + −

Question 7:2 2 2 3 10 lim x 4 x x  x − − −

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Question 8:4 3 2 81 lim x 2 5 3 x  x x − − −

Question 9:0 lim x 1 ax b  cx + +

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Question 10:1 3 1 1 6 1 lim 1 z z z  − −

Question 11:2 1 2 lim , 0 x ax bx c a b c  cx bx a + + + +  + +

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Question 12:2 1 1 lim 2 x 2 x − x + +

Question 13:0 sin lim x ax  bx

Question 14:0 sin lim , , 0 x sin ax a b  bx 

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Question 15:( )  ( ) sin  lim x   x  x − −

Question 16:0 cos lim x  x  − x

Question 17:0 cos 2 1 lim x cos 1 x  x − −

Question 18:0 cos lim x sin ax x x  b x +

Exercise 13.1 class 11 Math ncert solutions Chapter 13

Question 19:0 lim sec x x x 

Question 20:0 sin lim , , 0 x sin ax bx a b a b  ax bx + +  + ,

Question 21:0 lim (cosec cot ) x x x  −

EXERCISE 13.1 Evaluate the following limits in Ex

Question 22: 2 tan 2 lim  2 x x  x −

Question 23:Find ( ) 0 lim x f x  and ( ) 1 lim x f x  , where ( ) ( ) 2 3, 0 3 1 , 0 x x f x x x  +  =  + > 

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Question 24:Find ( ) 1 lim x f x  , where ( ) 2 2 1, 1 1, 1 x x f x x x

 −  = 

− − >

Question 25:Evaluate ( ) 0 lim x f x  , where ( ) | | , 0 0, 0 x x f x x x   =   =

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Question 26:Find ( ) 0 lim x f x  , where ( ) , 0 | | 0, 0 x x f x x x   =   =

Question 27:Find ( ) 5 lim x f x  , where f (x) = | x | −5

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Question 28:Suppose ( ) , 1 4, 1 , 1 a bx x f x x b ax x + <  = = 

 − > and if 1 lim x f (x) = f (1) what are possible values of a and b?

Question 29:Let a1, a2, . . ., an be fixed real numbers and define a function f (x) = (x − a1 ) (x − a2 )...(x − an ) . What is 1 lim xa f (x) ? For some a  a1, a2, ..., an, compute lim xa f (x).

Question 30:If ( ) 1, 0 0, 0 1, 0 x x f x x x x  + < = = 

 − > . For what value (s) of a does lim xa f (x) exists?

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Question 31:If the function f(x) satisfies ( ) 1 2 2 lim  x 1 f x  x − = − , evaluate ( ) 1 lim x f x  .

Question 32:If ( ) 2 3 , 0 , 0 1 , 1 mx n x f x nx m x nx m x  + <

= +   

 + > . For what integers m and n does both ( ) 0 lim x f x  and ( ) 1 lim x f x  exist?