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Byju's Answer
Standard XII
Mathematics
Derivative of Standard Functions
If f x = x ...
Question
If
f
(
x
)
=
⎧
⎨
⎩
x
p
cos
1
x
,
x
≠
0
0
,
x
=
0
, then at
x
=
0
,
f
(
x
)
is
A
continuous if
p
>
0
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B
differentiable if
p
>
1
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C
continuous if
p
>
1
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D
differentiable if
p
>
0
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Solution
The correct options are
A
continuous if
p
>
0
B
differentiable if
p
>
1
Continuity at
x
=
0
L
.
H
.
L
.
=
lim
h
→
0
f
(
0
−
h
)
=
lim
h
→
0
(
−
h
)
p
cos
1
h
=
0
if
p
>
0
R
.
H
.
L
.
=
lim
h
→
0
f
(
0
+
h
)
=
lim
h
→
0
h
p
cos
1
h
=
0
if
p
>
0
and,
f
(
0
)
=
0.
∴
f
(
x
)
is continuous at
x
=
0
if
p
>
0
L
f
′
(
0
)
=
lim
h
→
0
f
(
0
−
h
)
−
f
(
0
)
−
h
=
lim
h
→
0
(
−
h
)
p
cos
1
h
−
0
−
h
=
lim
h
→
0
(
−
h
)
p
−
1
cos
1
h
=
0
if
p
>
0
,
and,
R
f
′
(
0
)
=
lim
h
→
0
f
(
0
+
h
)
−
f
(
0
)
h
=
lim
h
→
0
h
p
cos
1
h
−
0
h
=
lim
h
→
0
h
p
−
1
cos
1
h
=
0
if
p
>
0
∴
f
(
x
)
is differentiable at
x
=
0
if
p
>
1.
Suggest Corrections
0
Similar questions
Q.
Show that the function
f
x
=
x
m
sin
1
x
,
x
≠
0
0
,
x
=
0
(i) differentiable at x = 0, if m > 1
(ii) continuous but not differentiable at x = 0, if 0 < m < 1
(iii) neither continuous nor differentiable, if m ≤ 0
Q.
If
f
(
x
)
=
p
|
sin
x
|
+
q
e
|
x
|
+
r
|
x
|
3
and if
f
(
x
)
is differentiable at
x
=
0
, then
Q.
f
(
x
)
=
x
m
S
i
n
(
1
4
)
if x
≠
0
0 if x=0 is continuous but not differentiable at x=0 then find the value of 'm'.
Q.
If
f
(
x
)
=
p
|
s
i
n
x
|
+
q
e
|
x
|
+
r
|
x
|
3
and if f(x) is differentiable at x = 0, then :
Q.
If
f
(
x
)
=
{
x
sin
1
x
else where
0
x
=
0
,
then
f
(
x
)
is
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