The second-degree Maclaurin polynomial for is

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

Problem

The second-degree Maclaurin polynomial for

\cos x

T_2(x)=1-\dfrac{x^{2}}{2}

. Find the greatest symmetric interval about

0

—expressed in the form

-R<x<R

—on which the approximation satisfies

|\cos x-T_2(x)|\le 1.0\times10^{-6}.

State the value of

R

to three significant figures.