# Review Questions for Taylor Series

- What is the general form of a Taylor series?
- How do you use a Taylor series to approximate a function at a given point?
- How can you approximate the derivative of a function using Taylor series?
- How can you approximate the integral of a function using Taylor series?
- Given an function and a cneter, can you write out the \(n\)-th degree Taylor polynomial?
- For an \(n\)-th degree Taylor polynomial, what is the bound on the error of your approximation as a function of distance from the center?
- For simple functions, can you find the constant \(C\) in the Taylor error bound?
- Be able to determine how many terms are required for a Taylor series approximation to have less than some given error.