Calculus 2 Quiz
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Consider approximating ee using the Maclaurin series for exe^x evaluated at x=1x=1, which is ∑n=0∞1n!\sum_{n=0}^\infty \frac{1}{n!}. We use the partial sum SN=∑n=0N1n!S_N = \sum_{n=0}^N \frac{1}{n!}. The Lagrange error bound for this approximation states that ∣RN∣≤M(N+1)!|R_N| \le \frac{M}{(N+1)!}, where MM is the maximum of ece^c on [0,1][0,1]. To use this bound, we need a value for MM, but ee is the number we are approximating. Which is the most effective and valid approach to establish a numerical error bound?
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