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 P3(x)=x−x36P_{3}(x)=x-\dfrac{x^{3}}{6}. Explain why the approximation error when using P3P_{3} at x=0.2x=0.2 is expected to be substantially smaller than the error at x=1x=1.

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