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Problem
Problem
The smallest natural number
k
k
k
for which
f
(
x
)
=
ln
(
x
3
+
x
6
+
1
)
+
sin
5
x
+
[
x
2
k
]
f(x)=\ln(x^3+\sqrt{x^6+1})+\sin 5x+\left[\frac{x^2}{k}\right]
f
(
x
)
=
ln
(
x
3
+
x
6
+
1
)
+
sin
5
x
+
[
k
x
2
]
is an odd function
∀
x
∈
[
−
2
π
,
2
π
]
\forall x\in[-2\pi,2\pi]
∀
x
∈
[
−
2
π
,
2
π
]
is (
[
y
]
[y]
[
y
]
denotes largest integer
≤
y
\le y
≤
y
) (a) 38 (b) 39 (c) 40 (d) 41
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