The Taylor series for a function f about x=0 converges to f for -1 ≤ q x ≤ q 1 . The n th-degree Taylor polynomial for f about x=0 is given by sumlimits _k=1n-1nfrac xkk2+k+1 . Of the following, which is the smallest number M for which the alternating series error bound guarantees that |f1-P_41| ≤ q M
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