Also,
lim
( )
x
c f x
→
 = lim
x
c x
c
→
=
Thus, lim
x
c
→ f(x) = c = f(c) and hence the function is continuous at every real number Having defined continuity of a function at a given point, now we make a natural
extension of this definition to discuss continuity of a function 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