The third‐degree Maclaurin polynomial for is used to approximate

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

Problem

The third‐degree Maclaurin polynomial

P_3(x)

for

e^{x}

is used to approximate

e^{0.2}

. On the interval

0\le x\le0.2

, suppose

e^{x}\le1.221

. Which of the following is the greatest possible error guaranteed by the Lagrange error bound? (a)

3.26\times10^{-4}

(b)

8.1\times10^{-5}

(c)

1.63\times10^{-3}

(d)

6.7\times10^{-5}