Review Questions for Taylor Series

1. What is the general form of a Taylor series?
2. How do you use a Taylor series to approximate a function at a given point?
3. How can you approximate the derivative of a function using Taylor series?
4. How can you approximate the integral of a function using Taylor series?
5. Given an function and a cneter, can you write out the \(n\)-th degree Taylor polynomial?
6. 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?
7. For simple functions, can you find the constant \(C\) in the Taylor error bound?
8. Be able to determine how many terms are required for a Taylor series approximation to have less than some given error.