1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XIII
Mathematics
Differentiability
If fx = xk si...
Question
If
f
(
x
)
=
⎧
⎨
⎩
x
k
sin
(
1
x
)
,
x
≠
0
0
,
x
=
0
is differentiable at
x
=
0
,
then (where
k
is an integer)
A
k
>
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
k
>
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
k
≥
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
k
≥
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
B
k
>
1
At
x
=
0
R.H.D.
=
lim
h
→
0
f
(
0
+
h
)
−
f
(
0
)
h
=
lim
h
→
0
h
k
sin
1
h
−
0
h
=
lim
h
→
0
h
k
−
1
sin
1
h
For this limit to exist, exponent of
h
must be positive.
i.e.,
k
−
1
>
0
⇒
k
>
1
Suggest Corrections
0
Similar questions
Q.
If
f
(
x
)
=
⎧
⎨
⎩
x
k
sin
(
1
x
)
,
x
≠
0
0
,
x
=
0
is differentiable at
x
=
0
,
then (where
k
is an integer)
Q.
For
x
∈
R
, let
f
(
x
)
=
⎧
⎨
⎩
x
3
sin
(
1
x
)
,
x
≠
0
0
,
x
=
0
.
Then which of the following options is (are) TRUE?
Q.
If f(0)=0
and that
'f'
is differentiable at x = 0, and ‘k’ is a positive integer. Then
lim
x
→
0
1
x
[
f
(
x
)
+
f
(
x
2
)
+
f
(
x
3
)
+
…
…
+
f
(
x
k
)
]
Q.
If
f
(
x
)
=
[
x
sin
π
x
]
i
n
(
−
1
,
1
)
then
f
(
x
)
is
Q.
If
f
(
x
)
=
x
+
|
x
|
+
cos
(
[
π
2
]
x
)
and
g
(
x
)
=
sin
x
,
then which of the following option is INCORRECT ?
(where [.] denotes the greatest integer function)
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Introduction to Differentiability
MATHEMATICS
Watch in App
Explore more
Differentiability
Standard XIII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app