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.