## Math 122 - Chapter 11 Project / Study Guide

### In-Class Portion

1. Find the sum of the series by associating it with some Maclaurin series. Look at supplemental problem 25
2. The values of the first n derivatives of a function are given. Find the nth degree Maclaurin and Taylor series for the function.
3. Find a Maclaurin series for the given binomial. Look at 11.9.21
4. Find the radius and intervals of convergence. Two parts. Look at problems 11.8.7-29
5. Use a Maclaurin series to approximate a value to three decimal-place accuracy. Check your answer against your calculator.
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 11.10.5-8
7. Use a Maclaurin series to approximate an integral. Look at problems 11.10-29-32
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 11.9.1-9
9. Differentiate and integrate a power series, leaving the answer in power series notation.
10. True or false. Determine the validity of these statements about convergence and divergence of infinite series with positive terms. Look at supplemental problem 9.
11. 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