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. Find a Maclaurin series for the given binomial. Look at 10.9.17
4. Find the radius and intervals of convergence. Two parts. Look at problems 10.8.25-48.
5. 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.
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 10.10.5-8
7. 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
8. Differentiate and integrate a power series, leaving the answer in power series notation.
9. 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.