Approximate (radian measure) with the second-degree Maclaurin polynomial

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

Problem

Approximate

\cos 1

(radian measure) with the second-degree Maclaurin polynomial

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

. Determine the magnitude of (i) the Lagrange error bound and (ii) the alternating-series error bound at

x=1

, each rounded to three decimal places and listed in the order (i), (ii).