Continuity of a Function

A function f(x) is said to be continuous at a point  x=a if,
   
                   Point value = Left hand limit (LHL)= Right hand limit (RHL)

what is point value - it is the value of a function at a particular point, as here the value of                                                f(x)  at  x=a  is  f(a)  so f(a) is the point value of  f(x) at a .

what is LHL & RHL - see the graph let y=f(x) is continuous at x=a , now LHL is a point                                                    whose value  is slightly less than a  means [a-h] ,RHL is a point                                                           whose value is slightly greater than  a means [a+h].

Let us understand mathematically (see the graph),

let f(x) is a function,it will be continuous at x=a only when ,
         
                                       f(a) [point value] = f(a-h) [LHL] = f(a+h) [RHL]

h is a small quantity which tends to zero.

  

(A special Thanks to Mr. Animesh Bhunia for his helping hand )