I am following the nice article “Simpson’s rule is exact for quintics” by Louis A. Talman, in its computation of the error term for approximating integrals using Simpson’s rule. The article was published in the American Mathematical Monthly, vol 113 February 2006, pp. 144-155. Albertsons library is subscribed to the Monthly, so you can find the article there. You can also find it in Dr. Talman’s page. More details on Taylor’s formula can be found on section 8.9 of the book.

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[…] of Taylor’s theorem (and it may be a good idea to take a look at Talman’s paper; see here); but it won’t include the proof that the method of partial fractions decomposition works. […]

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[…] of Taylor’s theorem (and it may be a good idea to take a look at Talman’s paper; see here); but it won’t include the proof that the method of partial fractions decomposition works. […]