Mathematics

Mathematics

Problem

Approximate cos⁡1\cos 1 (radian measure) with the second-degree Maclaurin polynomial P2(x)=1−x22P_{2}(x)=1-\dfrac{x^{2}}{2}. Determine the magnitude of (i) the Lagrange error bound and (ii) the alternating-series error bound at x=1x=1, each rounded to three decimal places and listed in the order (i), (ii).

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