Rationalised 2023-24
CONTINUITY AND DIFFERENTIABILITY
107
Solution The function is defined at x = 0 and its value at x = 0 is 1 When x ≠ 0, the
function is given by a polynomial Hence,
lim0
( )
x
f x
→
 =
3
3
0
lim (
3)
0
3
3
x
x
→
+
=
+
=
Since the limit of f at x = 0 does not coincide with f(0), the function is not continuous
at x = 0 It may be noted that x = 0 is the only point of discontinuity for this function