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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
sin
x
x
f(x)=\dfrac{\sin x}{x}
f
(
x
)
=
x
sin
x
for
x
≠
0
x\neq0
x
=
0
. Which of the following sets describes all real numbers where
f
′
(
x
)
f'(x)
f
′
(
x
)
exists? a)
R
∖
{
π
2
+
k
π
∣
k
∈
Z
}
\mathbb R\setminus\{\tfrac{\pi}{2}+k\pi\mid k\in\mathbb Z\}
R
∖
{
2
π
+
k
π
∣
k
∈
Z
}
b)
R
∖
{
0
}
\mathbb R\setminus\{0\}
R
∖
{
0
}
c)
R
∖
{
k
π
∣
k
∈
Z
}
\mathbb R\setminus\{k\pi\mid k\in\mathbb Z\}
R
∖
{
k
π
∣
k
∈
Z
}
d)
R
\mathbb R
R
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