Definition 2 A real function f is said to be continuous if it is continuous at every point
in the domain of f This definition requires a bit of elaboration Suppose f is a function defined on a
closed interval [a, b], then for f to be continuous, it needs to be continuous at every
point in [a, b] including the end points a and b Continuity of f at a means
lim
( )
x
a f x
→+
= f (a)
and continuity of f  at b means
lim–
( )
x
b f x
→
= f(b)
Observe that lim
( )
x
a f x
→−
 and lim
( )
x
b f x
→+
do not make sense