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    Taylor and MacLaurin Series

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    A. The Taylor series for about is given by

    Since for all n, we have for all n, whence

    B. Below is a plot of along with the four-term Taylor approximation computed above.

    C. The first six terms of the Taylor expansion of are as follows:

    This is a much better approximation, especially close the origin, ...

    Solution Summary

    We compute the Taylor series of some functions and graph them along with the first few terms of the series.