## Math 122 - Chapter 9-10.3 Study Guide

1. Solve the differential equation. Two parts, one separable, one using integrating factor. Look at problems 9.1.9-24
2. Solve the initial value differential equation. Look at problems 9.1.27-32
3. Match the differential equation with the direction field. Twelve parts. Look at problem 9.2.9
4. Use the direction field to sketch the integral curve. Look at problem 9.2.19.
5. Find the general solution to the second order homogeneous differential equation. Two parts. Look at problems 9.4.3-16.
6. A function has the indicated derivatives. Write and simplify the fourth order Maclaurin series for the function.
7. A function has the indicated derivatives. Write the Taylor series for the function. You can leave the (x-a) in factored form, but simplify the coefficients.
8. Write the first five terms of the sequence, determine whether the sequence converges, and if so, find its limit. Two parts. Look at problems 10.2.5-22
9. Find the general term of the sequence, starting with n=1, determine whether the sequence converges, and if so, find its limit. Two parts. Look at problems 10.1.23-30
10. Use the difference of consecutive terms to show that a sequence is strictly montonic. Look at problems 10.3.1-6
11. Use the ratio of consecutive terms to show that a sequence is strictly montonic. Look at problems 10.3.7-12
12. Use differentiation to show that a sequence is strictly montonic. Look at problems 10.3.13-18

### Notes:

• The in-class portion of the exam is worth 70 points, the take home portion is worth 30 points.
• The take home portion of the exam is due the day after the in-class exam.
 1 2 3 4 5 6 7 8 9 10 11 12 Total 8 4 6 3 8 5 5 8 8 5 5 5 70