Question

What is an example of a Taylor Series?

Answer 1

World politics can be complicated. Distant economies change dramatically. Far away populations move their centers. Sometimes, it's better to focus on what is happening locally. The same may be said for complicated mathematical expressions. By looking at the localized behavior of a function, we can often gain amazing insights. This is where the Taylor series is really useful. Simply put, the Taylor series is a representation of a function that can help us do mathematics. Uses of the Taylor series include analytic derivations and approximations of functions.

Answer 2

Theorem 1 (Taylor-Maclaurin series). Suppose that f(x) has a power series expansion at x = a with radius of convergence R > 0, then the series expansion of f(x)  takes the form

$f(x)=∑_(k=0)^n▒〖1/k! f^k (c)〖(x-c)〗^k 〗$