1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Improper Integrals
For what valu...
Question
For what value of k is the function
f
x
=
sin
5
x
3
x
,
if
x
≠
0
k
,
if
x
=
0
is
continuous
at
x
=
0
?
Open in App
Solution
Given:
f
x
=
sin
5
x
3
x
,
if
x
≠
0
k
,
if
x
=
0
If
f
x
is continuous at x = 0, then
lim
x
→
0
f
x
=
f
0
⇒
lim
x
→
0
sin
5
x
3
x
=
k
⇒
lim
x
→
0
5
sin
5
x
3
×
5
x
=
k
⇒
5
3
lim
x
→
0
sin
5
x
5
x
=
k
⇒
5
3
×
1
=
k
⇒
k
=
5
3
Suggest Corrections
0
Similar questions
Q.
Determine the value of the constant k so that the function
f
x
=
sin
2
x
5
x
,
if
x
≠
0
k
,
if
x
=
0
is
continuous
at
x
=
0
.
Q.
Determine the value of the constant
k
so that the function
f
(
x
)
=
⎧
⎨
⎩
sin
2
x
5
x
,
if
x
≠
0
k
,
if
x
=
0
is continuous at
x
=
0
Q.
For what value of k is the function
f
x
=
sin
2
x
x
,
x
≠
0
k
,
x
=
0
continuous at x = 0?
Q.
For what value of
is the function defined by
continuous at
x
= 0? What about continuity at
x
= 1?