Math 122: Chapter 9 Exam Study Guide

1. Determine whether the series converges absolutely, converges conditionally, or diverges. You do not need to show work. 14 parts.
2. Find the summation. Look at telescoping and geometric series.
3. Determine the convergence or divergence of the sequence with the given n^th term. If the sequence converges, find its limit. 2 parts.
4. Find the summation. Look at telescoping and geometric series.
5. Find the radius and interval of convergence for the power series. Be sure to check the endpoints separately if necessary. 4 parts.
6. Combine the summations into a single summation.
7. The values for f^(k)(0) for an unknown function are given. Use them to write a Maclaurin polynomial. Use the Maclaurin polynomial to estimate the value of the function at a particular point. Find the relative error in your approximation. Find the maximum error in your approximation (the maximum value of the next derivative is supplied).
8. Use the given power series to find a new power series.
9. Differentiate a power series in summation form.
10. Integrate a power series in summation form.
11. Determine whether the sequence is increasing or decreasing and whether it is bounded or unbounded.
12. Write the first four non-zero terms (before writing the ...) in the power series expansion by making a substitution into a known Maclaurin series. Also give the interval of convergence. 4 parts.
13. Find the first four non-zero terms in the Taylor series for the indicated function centered at the given point.
14. Write an expression for the n^th term of the sequence. There may be more than one correct answer. 4 parts.

Notes

• There are 106 possible points, which means that you can miss 6 points without hurting your grade.
• You should bring paper for work. Write your answers on the exam itself.

Points per problem

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Last updated April 17, 2011 8:56 AM