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Mathematics
Problem
The third-degree Maclaurin polynomial for
sin
x
\sin x
sin
x
is
P
3
(
x
)
=
x
−
x
3
6
P_{3}(x)=x-\dfrac{x^{3}}{6}
P
3
(
x
)
=
x
−
6
x
3
. Explain why the approximation error when using
P
3
P_{3}
P
3
at
x
=
0.2
x=0.2
x
=
0.2
is expected to be substantially smaller than the error at
x
=
1
x=1
x
=
1
.
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