For , the second-degree Maclaurin polynomial is . Find the greatest with such that…

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

Problem

For

f(x)=\sqrt{1+x}

, the second-degree Maclaurin polynomial is

P_2(x)=1+\dfrac{x}{2}-\dfrac{x^{2}}{8}

. Find the greatest

R

with

0<R<1

such that

|f(x)-P_2(x)|\le 5.0\times10^{-4}\quad\text{whenever }|x|\le R.

Report

R

to two decimal places.