Example 2 Examine whether the function f given by f(x) = x2 is continuous at x = 0 Solution First note that the function is defined at the given point x = 0 and its value is 0 Then find the limit of the function at x = 0 Clearly
2
2
0
0
lim
( )
lim
0
0
x
x
f x
x
→
=→
=
=
Thus
lim0
( )
0
(0)
x
f x
f
→
=
=
Hence, f is continuous at x = 0