A Maclaurin polynomial of degree is used to approximate at

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

A Maclaurin polynomial of degree

n

is used to approximate

\cos x

x=2

. Because all derivatives of

\cos x

and

\sin x

have magnitude at most

1

, find the least integer

n

for which the approximation error is guaranteed to be below

1.0\times10^{-5}

. Briefly justify that your value of

n

works.