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## Homework Statement

This is not a homework problem but I would like to clarify my concern.

It is stated that a function can be written as such:

[itex] f(x) = \lim_{n \rightarrow ∞} \sum^{∞}_{k=0} f^{(k)} \frac{(x-x_{0})^k}{k!} [/itex]

[itex] R_{n}=\int^{x}_{x_{0}} f^{(n+1)} (t) \frac{(x-t)^n}{n!} dt [/itex]

They state that by MVT,

[itex] R_{n}= \frac{f^{(n+1)}(x^{*})}{(n+1)!} (x-x_{0})^{n+1} [/itex]

For some [itex] x^{*} \in (x_{0},x) [/itex]

I am wondering which statement of MVT leads to the second identity? Much thanks:)

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