The third-degree Maclaurin polynomial for is

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

Problem

The third-degree Maclaurin polynomial for sin⁡x\sin x is T3(x)=x−x36T_3(x)=x-\dfrac{x^{3}}{6}. Determine the largest real number R>0R>0 such that ∣sin⁡x−T3(x)∣≤1.0×10−5whenever ∣x∣≤R.|\sin x-T_3(x)|\le 1.0\times10^{-5}\quad\text{whenever }|x|\le R. Give RR to three decimal places.

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