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JEE Advanced 2016 Paper 2 Mathematics Q7
Mathematics
Problem
Let
f
(
x
)
=
lim
n
→
∞
(
n
n
(
x
+
n
)
(
x
+
n
2
)
⋯
(
x
+
n
n
)
n
!
(
x
2
+
n
2
)
(
x
2
+
n
2
4
)
⋯
(
x
2
+
n
2
n
2
)
)
x
/
n
\displaystyle f(x)=\lim_{n\to\infty}\left(\frac{n^n(x+n)\left(x+\frac n2\right)\cdots\left(x+\frac nn\right)}{n!\,(x^2+n^2)\left(x^2+\frac{n^2}{4}\right)\cdots\left(x^2+\frac{n^2}{n^2}\right)}\right)^{x/n}
f
(
x
)
=
n
→
∞
lim
n
!
(
x
2
+
n
2
)
(
x
2
+
4
n
2
)
⋯
(
x
2
+
n
2
n
2
)
n
n
(
x
+
n
)
(
x
+
2
n
)
⋯
(
x
+
n
n
)
x
/
n
, for all
x
>
0
x>0
x
>
0
. Then
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