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. Differentiate and integrate a power series, leaving the answer in power series notation.
4. Find the radius and intervals of convergence. Two parts. Look at problems 10.8.25-48.
5. 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.
6. Find a Maclaurin series for the given binomial. Look at 10.9.17
7. Use known Maclaurin series to find the series for a product or quotient. Look at problems 10.10.13-16.
8. 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.
9. 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

Notes:

• Problems 1 - 5 are to be worked without a table of known Maclaurin series. When you are done with that part, turn it in and get the second part of the test. You can use a known table of Maclaurin series on the second part of the test. That table will be provided to you.
• There is a take home exam worth 13 points. This is due the day of the in-class exam.
• There is a classroom presentation and associated problems worth 29 points.
• The in-class test is worth 58 points.

Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 Total 9 5 6 8 12 4 4 5 5 58