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Taylor Series
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One of the most powerful tolls math has to offer for approximating functions
The Taylor series of a real or complex-valued function f(x)f(x) that is infinitely differentiable at a real or complex number aa is the power series:
n=0f(n)(a)n!(xa)n\sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(x-a)^n
The video below is an excellent reference about the topic: