# Math 122: Chapter 9.1-10.3 Study Guide

1. Separate and solve the differential equation. Look at problems 9.1.15-24.
2. Solve the differential equation using the method of integrating factors. Look at problems 9.1.9-14.
3. Solve the initial value problem using any method. Look at problems 9.1.27-32.
4. Find all values of r that yield solutions to the differential equation. Example, let y=xr. Find the solutions to x2y"+4xy'+2y=0. Begin by finding y' and y" and substituting into the equation. Then solve for r.
5. Find the solution to the second order differential equation. Look at problems 9.4.3-22. Three parts: find the general solution for two of them and solve the initial value problem for the third.
6. Given a direction field and an initial value, sketch the solution to the problem. Look at problems 9.2.3, 5.
7. Match the differential equation with the direction field. Six parts. Look at problem 9.2.9.
8. Find the first four partial sums for the indicated series.
9. Write the first five terms of the sequence and determine whether or not the sequence converges. If it converges, find its limit. Three parts. Look at problems 10.1.5-22.
10. Find the general term of the sequence, beginning with n=1. Determine whether or not the sequence converges. If it converges, find its limit. Two parts. Look at problems 10.1.23-30.
11. Determine whether the sequence is strictly increasing or strictly decreasing using the method described. Methods can include the difference of consecutive terms, the ratio of consecutive terms, or differentiation. Three parts. Look at problems 10.2.1-18.
12. Use any method to determine whether the sequence is eventually strictly increasing or eventually strictly decreasing.
13. Determine if the series converges, and if so, find its sum.
14. Use Euler's Method with the given step size to approximate the solution of the initial-value problem. Present your answer as a table and a graph. Use Microsoft Excel to create the table and graph. Place each problem on a separate worksheet within the same file and email it to the instructor.
15. Use WinPlot to sketch the slope fields and plot the solution curve to the initial-value problem. Be sure to generate the solution curves with both a positive and negative step size to get the entire curve. Save the graphs and email them to the instructor.

## Notes

• There is a take home portion of the exam worth 14 points.
• The take home exam is due the day of the in-class test.
• The last two problems on the in-class exam will be done using the computer. The computer may not be used for the first part of the exam.
• Many of the problems are very similiar to problems from the text (not necessarily odd).

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 4 4 4 4 9 3 6 3 9 6 9 3 10 6 6 86