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Byju's Answer
Standard XII
Mathematics
Distance Formula
Find whether ...
Question
Find whether
f
is continuous at
x
=
0
or not.If
f
is continous write 1 otherwise write 0 ?
What is the value of
f
(
x
)
at
x
=
0
Open in App
Solution
f
(
x
)
=
l
n
(
x
)
1
√
x
Applying L'Hospital's rule we get
=
1
x
−
1
2
x
√
x
=
−
2
√
x
Hence as
x
→
0
f
(
x
)
→
0
.
Thus
L
H
L
=
R
H
L
=
0
which is equal to the value of the
f
(
x
)
at
x
=
0
Hence
f
(
x
)
is continuous at
x
=
0
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0
Similar questions
Q.
f
(
x
)
=
|
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|
x
x
≠
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0
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Check whether
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Q.
Given that
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and
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, the value of
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Q.
Let
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x
=
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+
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a
-
log
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-
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b
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Q.
f
(
x
)
=
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x
)
1
/
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,
f
o
r
x
≠
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=
e
2
,
f
o
r
x
=
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}
at
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=
0
.Find whether
f
(
x
)
is continuous or not
Q.
I
f
f
(
x
)
=
∫
x
−
1
|
t
|
d
t
,
x
≥
−
1
,
t
h
e
n
[MNR 1994]