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JEE Advanced 2017 Paper 1 Mathematics Q9
Mathematics
Problem
Let
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
be differentiable such that
f
(
0
)
=
0
f(0)=0
f
(
0
)
=
0
,
f
(
π
/
2
)
=
3
f(\pi/2)=3
f
(
π
/2
)
=
3
and
f
′
(
0
)
=
1
f'(0)=1
f
′
(
0
)
=
1
. If
g
(
x
)
=
∫
x
π
/
2
[
f
′
(
t
)
csc
t
−
cot
t
csc
t
f
(
t
)
]
d
t
g(x)=\int_x^{\pi/2}[f'(t)\csc t-\cot t\csc t\,f(t)]\,dt
g
(
x
)
=
∫
x
π
/2
[
f
′
(
t
)
csc
t
−
cot
t
csc
t
f
(
t
)]
d
t
for
x
∈
(
0
,
π
/
2
]
x\in(0,\pi/2]
x
∈
(
0
,
π
/2
]
, then
lim
x
→
0
g
(
x
)
\lim_{x\to0}g(x)
lim
x
→
0
g
(
x
)
is
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