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Sin 1 over x/Primitive function/Consider x^2 cos 1 over x/Exercise
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We consider the function
f
:
R
⟶
R
,
t
⟼
f
(
t
)
,
{\displaystyle f\colon \mathbb {R} \longrightarrow \mathbb {R} ,t\longmapsto f(t),}
with
f
(
t
)
=
{
0
for
t
=
0
,
sin
1
t
for
t
≠
0
.
{\displaystyle {}f(t)={\begin{cases}0{\text{ for }}t=0,\\\sin {\frac {1}{t}}{\text{ for }}t\neq 0\,.\end{cases}}\,}
Show, with reference to the function
g
(
x
)
=
x
2
cos
1
x
,
{\displaystyle {}g(x)=x^{2}\cos {\frac {1}{x}}\,,}
that
f
{\displaystyle {}f}
has an antiderivative.
Create a solution