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Mathematics
Mathematics
Problem
If
[
x
]
[x]
[
x
]
denotes the greatest integer function then the extreme values of the function
f
(
x
)
=
[
1
+
sin
x
]
+
[
1
+
sin
2
x
]
+
⋯
+
[
1
+
sin
n
x
]
f(x) = [1 + \sin x] + [1 + \sin 2x] + \dots + [1 + \sin nx]
f
(
x
)
=
[
1
+
sin
x
]
+
[
1
+
sin
2
x
]
+
⋯
+
[
1
+
sin
n
x
]
,
n
∈
I
+
n \in I^+
n
∈
I
+
,
x
∈
(
0
,
π
)
x \in (0, \pi)
x
∈
(
0
,
π
)
are a.
(
n
−
1
)
(n-1)
(
n
−
1
)
b.
n
n
n
c.
(
n
+
1
)
(n+1)
(
n
+
1
)
d.
(
n
+
2
)
(n+2)
(
n
+
2
)
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