Using the third-degree Maclaurin polynomial for

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

Problem

Using the third-degree Maclaurin polynomial for tan⁡−1x=x−x33+x55−…\tan^{-1}x = x - \dfrac{x^{3}}{3}+\dfrac{x^{5}}{5}-\dots, compute (i) the Lagrange error bound and (ii) the alternating-series error bound for estimating tan⁡−1(0.3)\tan^{-1}(0.3). State both bounds to three significant figures, separated by a semicolon.

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