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Byju's Answer
Standard XII
Mathematics
Existence of Limit
Find limx→ ...
Question
Find
lim
x
→
1
f
(
x
)
,
where
f
(
x
)
=
{
x
2
−
1
,
x
≤
1
−
x
2
−
1
,
x
>
1
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Solution
f
(
x
)
=
{
x
2
−
1
,
x
≤
1
−
x
2
−
1
,
x
>
1
L.H.L
=
lim
x
→
1
−
f
(
x
)
=
lim
x
→
1
[
x
2
−
1
]
=
1
2
−
1
=
1
−
1
=
0
R.H.L
=
lim
x
→
1
+
f
(
x
)
=
lim
x
→
1
[
−
x
2
−
1
]
=
−
1
2
−
1
=
−
1
−
1
=
−
2
Clearly L.H.L
≠
R.H.L
Hence
lim
x
→
1
f
(
x
)
does not exist.
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