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 Example 3 Discuss the continuity of the function f given by f(x) = | x | at x = 0 Solution By definition
f(x) =
, if
0
, if
0
x
x
x
x
−
<

≥

Clearly the function is defined at 0 and f(0) = 0