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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 26
Total: 72
Find
lim
x→0
 f (x) , where f (x) = {
x
|x|
x≠0
0x=0
Solution:  
We have, f (x) = {
x
|x|
x≠0
0x=0
Now,
lim
x→0−
 f (x) =
lim
x→0−
x
|x|
 =
lim
x→0−
 (
x
−x
) [Since |x| = - x , for x < 0]
=
lim
x→0−
 ( - 1) = - 1
and
lim
x→0+
 f (x) =
lim
x→0+
x
|x|
 =
lim
x→0+
x
x
 [Since |x| = x , for x > 0]
=
lim
x→0+
 (1) = 1
Thus
lim
x→0−
 f (x) ≠
lim
x→0+
 f (x)
∴
lim
x→0
 f (x) does not exist.
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