# Taylor Series

- Power series allow us to represent associated functions on an appropriate interval.
- By the end of this section you should be able to do the following:
- Represent a function as a Taylor series or a Maclaurin series.
- Interpret Taylor series and Maclaurin series.
- Represent a function at a point as a Taylor polynomial.
- Approximate function values using a Taylor polynomial.

- By the end of this section you should know the following:
- There is a formula for finding the coefficient of the nth degree term in a Taylor polynomial (see below).
- In many cases, as the degree of a Taylor polynomial increases, the nth degree polynomial will approach the original function over some interval.
- Taylor polynomials for a function f centered at x = a can be used to approximate function values of f near x = a.
- A Taylor polynomial for
*f(x)*is a partial sum of the Taylor series for*f(x)*. - The Maclaurin series for 1/(1-x) is a geometric series.
- The Maclaurin series for sin x , cos x, and e^x provides the foundation for constructing the Maclaurin series for other functions.

- By the end of this section you should be able to do the following:

## Essential Questions

Essential Questions

### How are Taylor polynomials constructed?

How are Taylor polynomials constructed?