# Math 122 - Chapter 10 Study Guide

1. Determine whether or not the series converges, and if so, find its sum. Three parts. Look at problems 10.4.3-14
2. Find the Maclaurin series for the function by differentiation. Write the series in sigma notation. Look at problems 10.8.1-10.
3. Find a Maclaurin series for the given binomial. Look at 10.9.17
4. Find the radius and intervals of convergence. Two parts. Look at problems 10.8.25-48.
5. Use a Maclaurin series to approximate a value to three decimal-place accuracy. Check your answer against your calculator and find the percent error in the approximation. Look at problems 10.9.1-8.
6. Obtain the first four non-zero terms of a Maclaurin series by making an appropriate substitution into a known series. State the radius of convergence of the infinite series. Look at problem 10.10.5-8
7. Differentiate and integrate a power series, leaving the answer in power series notation.
8. Use known Maclaurin series to find the series for a product or quotient. Look at problems 10.10.13-16.
9. Identify each series as convergent, conditionally convergent, or divergent. Justify your answer. Four parts. Look at the problems from sections 10.5 through 10.7.

## Notes:

• There is a take home [PDF] exam worth 45 points. The take home portion includes two problems worth 15 points and a classroom presentation and homework assigned / graded by other students worth 30 points.
• A table a common Maclaurin series will be provided on the exam.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 Take Home Total 9 4 4 8 4 4 6 4 12 45 100