Let be the th-degree Maclaurin polynomial for

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

Problem

Let

T_n(x)

be the

n

th-degree Maclaurin polynomial for

e^{2x}

. For all

x

[-0.2,0.2]

, what is the least integer

n

that guarantees the relative error

\displaystyle \bigl|\tfrac{e^{2x}-T_n(x)}{e^{2x}}\bigr|

is less than

1\times10^{-4}

? (a)

n=3

(b)

n=5

(c)

n=4

(d)

n=7