Question

pls help me to prove taylors theorem

Answer 1

Hey dude here is your answer.....

Answer 2

Answer:

I am having trouble understanding the intuition behind the last part of this theorem. I'd appreciate some help understanding the intuition behind the last equation: f(β)=P(β)+f(n)(x)n!(β−α)n. Why are we concerned about the end point β, and what is the (intuitive) relationship between f(β) and P(β)?

Here is the theorem typed out:

Suppose f is a real function on [a,b], n is a positive integer, fn−1 is continuous on [a,b], f(n)(t) exists for every t∈(a,b). Let α,β be distinct points of [a,b], and define

P(t)=∑n−1k=0f(k)(α)k!(t−α)k

Then there exists a point x between α and β such that

f(β)=P(β)+f(n)(x)n!(β−α)n.

pls mark me as the brainliest

              :)