# Math 122 - Chapter 10 Study Guide

- Determine whether or not the series converges, and if so, find its sum.
Three parts. Look at problems 10.4.3-14
- Find the Maclaurin series for the function by differentiation. Write the
series in sigma notation. Look at problems 10.8.1-10.
- Differentiate and integrate a power series, leaving the answer in power
series notation.
- Find the radius and intervals of convergence. Two parts. Look at problems
10.8.25-48.
- 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.
- Find a Maclaurin series for the given binomial. Look at 10.9.17
- Use known Maclaurin series to find the series for a product or quotient.
Look at problems 10.10.13-16.
- 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.
- 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

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Total |

Pts |
9 |
5 |
6 |
8 |
12 |
4 |
4 |
5 |
5 |
58 |