Taylor Series

Overview

The Taylor series of a function {% f %} is a polynomial that converges to the function under certain conditions.
{% Taylor \, Polynomial \, of \, f(x) = \sum_{k} \frac{f^{(k)}(a)}{k!} (x-a)^k %}
A Taylor polynomial of order n is the first n terms in the Taylor polynomial given above. It assumes that the first n derivatives of the function exists at the given point.

Taylor Example

In the following example, we examine the taylor series of the sine function. The slider lets you select the number of derivatives to use in the taylor approximation. (between 0 and 20)


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