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 Hence we may also rephrase  the definition of
continuity as follows: a function is continuous at x = c if the function is defined at
x = c and if the value of the function at x = c equals the limit of the function at
x = c If f is not continuous at c, we say f is discontinuous at c and c is called a point
of discontinuity of f