## Last Midterm

## Fall 2001

1. Use the power series representation of e^{z} to
approximate

to the nearest thousandth.

2. Evaluate

3. Does the following series converge? Why?

4. Find the radius of convergence of

5. Find the power series representation for tan*x* using

- a. the Maclaurin series
- b. dividing the power series for the cosine into the power
series for the sine.

Find an estimate for the error in the 5th degree polynomial
approximation of

using Taylor's Theorem.

(Extra Credit) Find a formula for the coefficients in the power
series for the tangent.