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Accuracy and Tolerance

To measure how well a Taylor Polynomial approximates the function over a specified interval $[c,d]$, we define the tolerance $Tol$ of $P_n(x,a)$ to be the maximum of the absolute error

\begin{displaymath}\mid f(x)- P_n(x,a) \mid \end{displaymath}

over the interval $[c,d]$.

William W. Farr