For , what is the coefficient of in the third-degree Taylor polynomial of centered at…

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

Problem

For

g(x)=e^{2x}

, what is the coefficient of

(x-1)^3

in the third-degree Taylor polynomial of

g

centered at

x=1

? (a)

8e^{2}

(b)

\dfrac{4}{3}e^{2}

(c)

\dfrac{8}{3}e^{2}

(d)

\dfrac{2}{3}e^{2}