The series expansion for on is

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

Problem

The series expansion for

\arctan x

|x|\le 1

x-\dfrac{x^{3}}{3}+\dfrac{x^{5}}{5}-\cdots

. Using only the cubic polynomial

x-\dfrac{x^{3}}{3}

, determine all real numbers

x

in the interval

[0,1]

for which the magnitude of the remainder is less than

0.01

. Give the largest such value of

x

correct to two decimal places.