MATH 1020U Chapter 15: mod10b_taylorseries
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Taylor and maclaurin series (section 11. 10 of stewart) Recall: in calc i/intro calc, we studied linear (and quadratic) approximations to a function. The more terms we included in our approximation, the better the approximation was. Definition: if f has a power series expansion at a, then it must be of the form: xf n. 0 f n a n ax n af af. 3 which is called the taylor series of the function f at a. A special case that occurs often is when. , so we give it a special name: the xf n. Example: find the maclaurin series for xf xe. Enrichment example: find the maclaurin series for xf sin x. So far, we"ve found taylor and maclaurin series for very simple functions, but we can use these results to find the series for more complicated functions. Example: given that the maclaurin series for xf xe expansion for xf.
