Mathematics

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}