Module 2 : Limits and Continuity of  Functions
Lecture 5 : Continuity  [ Section 5.1 : Extending the Limit concept ]
5.1  
Extending the limit concept
5.1 .1  
Definition :
 
(i) We write    if for every there is some such that for every

                                           

(ii) We write if for every  there is some  such that  ,

                                             .
5.1 .2  
Examples :
 

(i)  , since for a given,  we can choose as per requirements.

 

(ii)  .

5.1 .3
Definitions :
 
(i)  if for every , there exists some  such that 

                                         implies  .
(ii)   if for every , there exists some  such that 

                                         implies .
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