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Problem
Problem
If
f
(
x
)
=
1
3
(
f
(
x
+
1
)
+
5
f
(
x
+
2
)
)
f(x) = \frac{1}{3} \left( f(x+1) + \frac{5}{f(x+2)} \right)
f
(
x
)
=
3
1
(
f
(
x
+
1
)
+
f
(
x
+
2
)
5
)
and
f
(
x
)
>
0
,
∀
x
∈
R
f(x) > 0, \forall x \in \mathbb{R}
f
(
x
)
>
0
,
∀
x
∈
R
, then
lim
x
→
∞
f
(
x
)
\lim_{x \to \infty} f(x)
lim
x
→
∞
f
(
x
)
is a. 0 b.
2
5
\sqrt{\frac{2}{5}}
5
2
c.
5
2
\sqrt{\frac{5}{2}}
2
5
d.
∞
\infty
∞
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