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Chapter 13 Limits and Derivatives Ex 13.1 Solutions

Question - 21 : - Evaluate the given limit:

Answer - 21 : -


Question - 22 : - Evaluate the given limit:

Answer - 22 : -


Question - 23 : -

Answer - 23 : -


Question - 24 : - Find<img src="data:image/png;base64,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" alt="">where 

Answer - 24 : -


Question - 25 : -
Evaluate
 , where f(x) =

Answer - 25 : -


Question - 26 : -
Find
 , where f (x) =

Answer - 26 : -


Question - 27 : -
Find
 , where

Answer - 27 : -


Question - 28 : -
Suppose
 and if
 what are possible values of a and b

Answer - 28 : -


Question - 29 : -

Let a1, a2,………an befixed real numbers and define a function

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

What is 

 For some a ≠ a1, a2, ……. an, compute

 

Answer - 29 : -


Question - 30 : - If   For what value (s) of a does  exists?

Answer - 30 : -


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