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Concept of Continuity

 
For finding  we find


 

 

1.     (i) Right Hand Limit, denoted by
 

             Working Rule:
 

             Replace x by (a + h) and take the limit as h à 0.

       

        (ii) Left Hand Limit, denoted by

 

             Working Rule:

 

             Replace x by (a – h) and take the limit as h à 0.
 

       

        (iii) Conclusion:
 

             If f (a + 0) = f (a – 0), then their common value is

 

             If f (a + 0)  f (a – 0), we say that  does not exist.
 

 

2.             A function f (x) is said to be continuous at x = a, if
 

        
 

 

        i.e., f (a + 0) = f (a – 0) = f (a)

 

        If f (x) is not continuous at x = a, we say that it is discontinuous at x = a





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