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The Taylor expansion is the series expansion of a function at a point. It represents a function as an infinite sum with terms calculated from the functions derivatives at that point. It is defined as \begin{equation*} \sum^{\infty}_{n=0}\frac{f^{(n)}(a)}{n!}(x-a)^n=f(a)+\frac{f'(a)}{1!}(x-a)+\frac{f''(a)}{2!}(x-a)^2+... \end{equation*}

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