Hello Tapabrota De!

According to my understanding, saying a function f is continuous when x = c is the same as saying that the function's two-side limit at x = c exists and is equal to f(c).

So it depends the given function, but it is necessary to prove that the left and right hand limit is equal to the value of the function at a point; it depends maybe stated otherwise. Then you've to show if the continuous of that point. 

-Hope you found this helpful,

~Galaxy. 

I agree, but given the question is to find the limit exists at the point 'c' or not; then should i be concerned about  exact value of f(c)?

TIA

Limits are only concerned with how the function behaves (arbitrarily) near a point. Limits are not concerned with what the actual value of the function is at the point.

For a limit to exist, the left and right hand limits need to be equal, but they do not need to be equal to the value of the function at the point. If they do happen to be equal to the value of the function at the point, then the function is said to be continuous at that point.

Also, if you can show that a function is continuous at a point c, then that suffices to show that the limit of f(x) as x approaches c exists.