Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
JEE Advanced 2016 Paper 2 Mathematics Q9
Mathematics
Problem
Let
f
:
R
→
(
0
,
∞
)
f:\mathbb R\to(0,\infty)
f
:
R
→
(
0
,
∞
)
and
g
:
R
→
R
g:\mathbb R\to\mathbb R
g
:
R
→
R
be twice differentiable functions such that
f
′
′
f''
f
′′
and
g
′
′
g''
g
′′
are continuous functions on
R
\mathbb R
R
. Suppose
f
′
(
2
)
=
g
(
2
)
=
0
f'(2)=g(2)=0
f
′
(
2
)
=
g
(
2
)
=
0
,
f
′
′
(
2
)
≠
0
f''(2)\ne0
f
′′
(
2
)
=
0
and
g
′
(
2
)
≠
0
g'(2)\ne0
g
′
(
2
)
=
0
. If
lim
x
→
2
f
(
x
)
g
(
x
)
f
′
(
x
)
g
′
(
x
)
=
1
\displaystyle\lim_{x\to2}\frac{f(x)g(x)}{f'(x)g'(x)}=1
x
→
2
lim
f
′
(
x
)
g
′
(
x
)
f
(
x
)
g
(
x
)
=
1
, then
Browse the problem library