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Math — Taylor Remainder

The Lagrange form of the truncation error.

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R_n = \frac{f^{(n+1)}(\xi)}{(n+1)!}(x - a)^{n+1}

\xi \in (a, x)

|R_n| \leq \frac{M|x-a|^{n+1}}{(n+1)!}

\text{bounds the truncation error}