A Taylor polynomial of degree 2 centered at is used to approximate near the origin

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

Problem

A Taylor polynomial of degree 2 centered at

x=0

is used to approximate

e^{x}

near the origin. Which of the following is the best upper bound for the magnitude of the error when

x=0.2

? (a)

3.26\times 10^{-3}

(b)

1.63\times 10^{-3}

(c)

1.33\times 10^{-3}

(d)

8.14\times 10^{-3}