Calculate pi using Taylor's theorem. Calculate the value of T u... | Filo

Proof of Taylor's TheoremProvide a proof of Taylor's theorem ... | Filo

SOLVED:Proof of Taylor's Theorem There are several proofs of Taylor's Theorem, which lead to various forms of the remainder. The following proof is instructive because it leads to two different forms of the remainder and it relies on the Fundamental Theorem of Calculus, integration by parts, and the Mean Value Theorem for Integrals. Assume that f has at least n 1 continuous derivatives on an interval containing a a. Show that the Fundamental Theorem of Calculus can be written in the form f(x)=f(