Question

Write the remainder after n term of

Taylor’s theorem in Cauchy’s form.
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Answer 1

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That is, as claimed, Rn(x) = (x - c)n-1(x - a) (n - 1)! f(n)(c) This result is Taylor's Theorem with the Cauchy remainder. There is another form of the remainder which is also useful, under the slightly stronger assumption that f(n) is continuous.

Answer 2

That is, as claimed, Rn(x) = (x - c)n-1(x - a) (n - 1)! f(n)(c) This result is Taylor's Theorem with the Cauchy remainder. There is another form of the remainder which is also useful, under the slightly stronger assumption that f(n) is continuous. f/(t)dt, so we're done by the FTC.