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Mathematics
Mathematics
Problem
Let
h
h
h
be the function defined by
h
(
x
)
=
{
x
3
sin
(
1
x
)
,
x
≠
0
,
0
,
x
=
0.
h(x)=\begin{cases} x^{3}\sin\left(\dfrac{1}{x}\right), & x\neq 0,\\ 0, & x=0. \end{cases}
h
(
x
)
=
⎩
⎨
⎧
x
3
sin
(
x
1
)
,
0
,
x
=
0
,
x
=
0.
Determine
h
′
(
0
)
h'(0)
h
′
(
0
)
, or state that the derivative does not exist.
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