6
  Fig 5 7
Rationalised 2023-24
 MATHEMATICS
112
Case 3 Now we analyse the function at x = 0 The value of the function at 0 is f(0) = 0 The left hand limit of  f at 0 is
–
2
2
0
0
lim
( )
lim
0
0
x
x
f x
−x
→
=→
=
=
The right hand limit of f at 0 is
0
0
lim
( )
lim
0
x
x
f x
x
+
+
→
=→
=
Thus 
lim0
( )
0
x
f x
→
=
= f(0) and hence f is continuous at 0