## Math 122 - Chapter 11 Project / Study Guide

### In-Class Portion

- Find the sum of the series by associating it with some Maclaurin series. Look at
supplemental problem 25
- The values of the first n derivatives of a function are given. Find the nth degree
Maclaurin and Taylor series for the function.
- Find a Maclaurin series for the given binomial. Look at 11.9.21
- Find the radius and intervals of convergence. Two parts. Look at problems 11.8.7-29
- Use a Maclaurin series to approximate a value to three decimal-place accuracy. Check
your answer against your calculator.
- 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 11.10.5-8
- Use a Maclaurin series to approximate an integral. Look at problems 11.10-29-32
- 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 11.9.1-9
- Differentiate and integrate a power series, leaving the answer in power series notation.
- True or false. Determine the validity of these statements about convergence and
divergence of infinite series with positive terms. Look at supplemental problem 9.
- Identify each series as convergent, conditionally convergent, or divergent. Justify your
answer. Four parts.

### Notes:

- There is a take home portion of the exam worth 35 points. The take home portion
includes a classroom presentation and homework assigned / graded by other students.
- A table a common Maclaurin series will be provided on the exam.

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
Total |

Pts |
4 |
6 |
4 |
8 |
4 |
5 |
7 |
4 |
6 |
5 |
12 |
65 |