Approximate using both the second-degree and the fourth-degree Taylor polynomials…

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

Problem

Approximate

\cos(0.5)

using both the second-degree and the fourth-degree Taylor polynomials centered at

x=0

. Which of these two approximations is within

10^{-6}

of the true value

\cos(0.5)\approx0.877582562

? State the approximation that meets the tolerance.