# Math 122 - Chapter 10 Study Guide

1. Use any method to determine whether the series converges or diverges. Indicate the method used. Five parts.
2. A table of values of k and f(k)(0) are given. Use them to find a Maclaurin polynomial for the function f. Approximate f(x) for some value of x close to 0. Then integrate the polynomial and use it to approximate a definite integral.
3. 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. Differentiate the polynomial and approximate it at a value close to x=a.
4. Differentiate and integrate a power series, leaving the answer in power series notation.
5. Find the radius and intervals of convergence. Three parts.
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. Three parts.
7. Manipulate a known Maclaurin series to find the series for a product or quotient.
8. Use a Taylor series to approximate a value.
9. Solve the initial value problem. It is a 2nd order homogeneous linear differential equation with constant coefficients.
10. Use the indicated method to rewrite the integral. Do not integrate. Look back at the techniques in sections 8.2 - 8.5.
11. Use Euler's method to solve the differential equation.
12. Write the series in sigma notation and determine if it converges. You may find the College Algebra lecture notes on sequences and series useful.
13. Differentiate. Three parts.
14. Integrate. Two parts.
15. Integrate using integration by parts (the tabular method may be useful).

## Notes

• You may use a table of known Maclaurin series on the exam. This will be provided to you during the exam.
• Problems 11-15 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 Total 30 10 10 8 18 15 5 7 7 15 5 10 15 10 10 175