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Manipal Entrance Test 2015 Math Paper
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© examsnet.com
Question : 32
Total: 70
If
f
(
x
)
=
{
sin
(
cos
x
)
−
cos
x
(
π
−
2
x
)
3
,
x
≠
π
2
k
,
x
=
π
2
is a continuous at
x
=
π
2
,
then k is equal to
0
−
1
6
−
1
24
−
1
48
Validate
Solution:
It is given that
f
(
x
)
is continuous at
x
=
π
2
.
∴
k
=
lim
x
→
π
∕
2
f
(
x
)
∴
k
=
lim
x
→
π
∕
2
sin
(
cos
x
)
−
cos
x
(
π
−
2
x
)
3
⇒
k
=
lim
x
→
π
∕
2
sin
(
cos
x
)
−
cos
x
cos
3
x
×
sin
3
(
π
2
−
x
)
8
(
π
2
−
x
)
3
∴
k
=
−
1
6
×
1
8
=
−
1
48
[
∵
lim
x
→
0
sin
x
−
x
x
3
=
−
1
6
]
© examsnet.com
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