# 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.
- Find a Maclaurin series for the given binomial. Look at 10.9.17
- Find the radius and intervals of convergence. Two parts. Look at
problems 10.8.25-48.
- 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
- Use the Remainder Estimation Theorem to find the smallest
*n* so
that the approximation is accurate to the given number of decimal places..
Look at problems 10.9.1-8
- Differentiate and integrate a power series, leaving the answer in power
series notation.
- 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 40 points. The take home portion includes
one problem worth 10 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.

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

Pts |
9 |
5 |
4 |
8 |
5 |
5 |
4 |
8 |
12 |
60 |