Question

State and proof of Taylor's theorem
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Answer 1

Answer:

Connection with Mean Value Theorem. When n = 0, Taylor's theorem reduces to the Mean Value Theorem which is itself a consequence of Rolle's theorem. A similar approach can be used to prove Taylor's theorem. Suppose that f has a stationary point at a and that f (a) = ··· = f(n−1)(a) = 0, while f(n)(a) = 0.

Step-by-step explanation:

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Answer 2

Answer:

Taylor's Series Theorem

Assume that if f(x) be a real or composite function, which is a differentiable function of a neighbourhood number that is also real or composite. Then, the Taylor series describes the following power series : f(x) =f(a)\frac{f'(a)}{1!}( x-a)+\frac{f”(a)}{2!}(