Consider . A student substitutes into and the fourth-degree Maclaurin polynomial for…

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

Problem

Consider

g(x)=x^{2}e^{x}

. A student substitutes

x=0.2

into

x^{2}

and the fourth-degree Maclaurin polynomial for

e^{x}

1+x+\dfrac{x^{2}}{2}+\dfrac{x^{3}}{6}+\dfrac{x^{4}}{24},

then multiplies the results to approximate

g(0.2)

. Which of the following values is closest to the student’s approximation? (a)

0.0549

(b)

0.0400

(c)

0.0489

(d)

0.0498