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Mathematics
Problem
The Maclaurin series for
e
x
2
e^{x^{2}}
e
x
2
is
∑
k
=
0
∞
x
2
k
k
!
\displaystyle\sum_{k=0}^{\infty}\dfrac{x^{2k}}{k!}
k
=
0
∑
∞
k
!
x
2
k
. Let
h
(
x
)
=
∫
0
x
e
t
2
d
t
h(x)=\displaystyle\int_{0}^{x} e^{t^{2}}\,dt
h
(
x
)
=
∫
0
x
e
t
2
d
t
. What is the coefficient of
x
5
x^{5}
x
5
in the Maclaurin series for
h
(
x
)
h(x)
h
(
x
)
? a)
1
8
\dfrac{1}{8}
8
1
b)
1
10
\dfrac{1}{10}
10
1
c)
1
5
\dfrac{1}{5}
5
1
d)
1
20
\dfrac{1}{20}
20
1
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