Naively, we may say that a function is
continuous at a fixed point if we can draw the
graph of the function around that point without
lifting the pen from the plane of the paper Mathematically, it may be phrased precisely as follows:
Definition 1 Suppose f is a real function on a subset of the real numbers and let  c be
a point in the domain of f Then f is continuous at c if
lim
( )
( )
x
c f x
f c
→
=
More elaborately, if the left hand limit, right hand limit and the value of the function
at x = c exist and equal to each other, then f is said to be continuous at x = c Recall that
if the right hand and left hand limits at x = c coincide, then we say that the common
value is the limit of the function at x = c