# 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. Use known Maclaurin series to find the series for a product or quotient. Look at problems 10.10.13-16.
9. Some terms and partial sums from a convergent alternating series are given. Determine an interval estimation for the sum as well as an upper bound on the error of the estimation. Use Theorem 10.6.2.
10. 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. Three parts. Look at problem 10.10.5-8
11. 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.

## 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 on the second part of the test. That table will be provided to you.
• There is a classroom presentation and associated problems worth 29 points.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 Total 4 4 6 4 12 16 4 3 4 6 8 71