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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 25
Total: 72
Evaluate
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
Since
lim
x→0−
 f (x) ≠
lim
x→0+
 f (x)
Thus
lim
x→0
 f (x) does not exist.
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