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KEAM 2018 Math Paper
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© examsnet.com
Question : 9
Total: 120
If
f
:
R
→
(
0
,
∞
)
is an increasing function and if ,
lim
x
→
2018
f
(
3
x
)
f
(
x
)
=
1
,
then
lim
x
→
2018
f
(
2
x
)
f
(
x
)
is equal to
2
3
3
2
2
3
1
Validate
Solution:
Given,
f
:
R
→
(
0
,
∞
)
is an increasing function.
And
lim
x
→
2018
f
(
3
x
)
f
(
x
)
=
1
So,
lim
x
→
2018
f
(
3
x
)
=
lim
x
→
2018
f
(
x
)
⇒
f
(
x
)
=
constant.
Therefore,
lim
x
→
2018
f
(
2
x
)
f
(
x
)
=
1
© examsnet.com
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