unl-taylorcont

unl-taylorcont - Analysis WebNotes Chapter 07 Class 46...

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Analysis WebNotes: Chapter 07, Class 46 1 of 3 11/9/2007 11:20 AM Class Contents Taylor series (continued) Discovering power series expansions for functions Mathematical implications Not all functions are Taylor series Taylor's theorem Examples Taylor Series Discovering Power Series Expansions for Functions We've already seen how incredibly useful it is to know the power series form for just one function: the exponential function e x . Many functions have power series expansions. For example: Other functions can be expressed as power series too: are two important examples. In order to verify that these function are equal to power series we will need to know in advance what power series we are trying to show the function is equal to. (Just as, in fact, we needed to know in advance what power series e x was equal to, although we just pulled the answer out of the hat.) Example.

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