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Byju's Answer
Standard XII
Mathematics
Continuity of a Function
Check continu...
Question
Check continuity
f
(
x
)
=
⎧
⎨
⎩
|
x
|
+
1
,
x
<
0
0
,
x
=
0
|
x
|
+
1
,
x
>
0
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Solution
at
x
=
0
R.H.L
lim
x
→
0
+
h
f
(
x
)
=
lim
h
→
0
|
h
|
+
1
=
lim
h
→
0
h
+
1
=
1
L.H.L
lim
x
→
0
−
h
f
(
x
)
=
lim
h
→
0
|
−
h
|
+
1
=
lim
h
→
0
h
+
1
=
1
and
f
(
0
)
=
0
Since R.H.L
=
L.H.L
so, limit exist at
x
=
0
since R.H.l
=
L.H.L
≠
f
(
0
)
Therefore
f
(
x
)
is not continuous at
x
=
0
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0
Similar questions
Q.
The function
f
(
x
)
=
{
1
4
x
−
1
,
x
≠
0
0
,
x
=
0
is continuous
Q.
Check the continuity of
f
(
x
)
=
{
(
1
+
3
x
)
1
/
x
x
≠
0
e
3
x
=
0
at
x
=
0
.
Q.
Discuss the continuity of the following functions at the indicated point(s):
(i)
f
x
=
x
cos
1
x
,
x
≠
0
0
,
x
=
0
at
x
=
0
(ii)
f
x
=
x
2
sin
1
x
,
x
≠
0
0
,
x
=
0
at
x
=
0
(iii)
f
x
=
(
x
-
a
)
sin
1
x
-
a
,
x
≠
a
0
,
x
=
a
at
x
=
a
(iv)
f
x
=
e
x
-
1
log
(
1
+
2
x
)
,
if
x
≠
a
7
,
if
x
=
0
at
x
=
0
(v)
f
x
=
1
-
x
n
1
-
x
,
x
≠
1
n
-
1
,
x
=
1
n
∈
N
at
x
=
1
(vi)
f
x
=
x
2
-
1
x
-
1
,
for
x
≠
1
2
,
for
x
=
1
at
x
=
1
(vii)
f
x
=
2
x
+
x
2
x
,
x
≠
0
0
,
x
=
0
at
x
=
0
Q.
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
(
3
sin
x
−
1
)
2
x
log
(
1
+
x
)
,
x
≠
0
2
log
3
,
x
=
0
Check continuity at
x
=
0
Q.
Check the continuity of the function
f
(
x
)
=
{
|
x
|
x
,
x
≠
0
0
,
x
=
0
at
x
=
0
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