# Math 122 - Chapter 10 Study Guide

1. Find the Maclaurin series for the function by differentiation. Write the series in sigma notation. Look at problems 10.7.7-16.
2. Differentiate and integrate a power series, leaving the answer in power series notation.
3. A table of values of k and f(k)(0) are given. Use them to find a Maclaurin polynomial for the function f. Then integrate the polynomial and use it to approximate a definite integral.
4. A table of values of k and f(k)(a) are given. Use them to find a Tayor polynomial for the function f centered about the point x=a. Use the polynomial to approximate f(x) for some value of x close to x=a.
5. Find the radius and intervals of convergence. Three parts. Look at problems 10.8.25-48.
6. Use the indicated test to determine the convergence or divergence of a series. If the test is inconclusive, say so. Eight parts (one for each of the tests). Look at the problems in 10.4 - 10.6. Show work so it can be verified that you're using the proper test.
7. Find a Maclaurin series for the given binomial. Look at 10.9.17.
8. Identify each series as absolutely convergent, conditionally convergent, or divergent. You may use any of the tests that you need. Four parts. Look at the problems from sections 10.4 through 10.6.
9. Solve the initial value problem.
10. Use Euler's method to solve the differential equation.
11. Write the series in sigma notation and determine if it converges. You may find the College Algebra lecture notes on sequences and series useful.
12. Integrate. Three parts.
13. Differentiate. Three parts.
14. Evaluate the limit. Two parts.
15. Use known Maclaurin series to find the series for a product or quotient. Look at problems 10.10.13-16.
16. 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. Two parts. Look at problem 10.10.5-8
17. Use a Taylor series to approximate a value.

## Notes

• Problems 1 - 4 are to be worked without a table of known Maclaurin series. When you are done with that part, turn it in and get the second part of the test.
• You can use a known table of Maclaurin series for problems 5 - 8. That table will be provided to you.
• Problems 9 - 17 are on a take home exam. They are not overly difficulty, I'm just trying to get the in-class portion short enough that you have enough time to do it. Work should be done on a separate piece of paper and attached. Copy the answers onto the test itself.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total 5 10 7 5 15 40 5 15 5 5 5 15 15 10 5 8 5 175