The remainder for the -degree Maclaurin polynomial of satisfies

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

Problem

The remainder for the

(2n+1)

-degree Maclaurin polynomial of

\arctan x

satisfies

|R_{2n+1}(x)|\le \dfrac{|x|^{\,2n+3}}{2n+3}

. Find the least degree necessary to approximate

\arctan(0.3)

with an error less than

10^{-6}