The Maclaurin series for is

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The Maclaurin series for

e^{x^{2}}

\displaystyle\sum_{k=0}^{\infty}\dfrac{x^{2k}}{k!}

. Let

h(x)=\displaystyle\int_{0}^{x} e^{t^{2}}\,dt

. What is the coefficient of

x^{5}

in the Maclaurin series for

h(x)

? (a)

\dfrac{1}{8}

(b)

\dfrac{1}{10}

(c)

\dfrac{1}{5}

(d)

\dfrac{1}{20}