Intro to Taylor Series: Approximations on Steroids
While in Calc I we used Linear Approximations, can we approximate functions by quadratics, cubics, etc? Indeed, Taylor Series (and Maclauren series when they are centered at x=0) provide a method for effective approximation of functions locally. And the best part is all we need to know is a lot of information about derivatives all at one point, and this is enough to get, typically, a decent approximation locally.
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