## Math 122 - Chapter 9-10.3 Study Guide

- Solve the differential equation. Two parts, one separable, one using
integrating factor. Look at problems 9.1.9-24
- Solve the initial value differential equation. Look at problems
9.1.27-32
- Match the differential equation with the direction field. Twelve parts.
Look at problem 9.2.9
- Use the direction field to sketch the integral curve. Look at problem
9.2.19.
- Find the general solution to the second order homogeneous differential
equation. Two parts. Look at problems 9.4.3-16.
- A function has the indicated derivatives. Write and simplify the fourth
order Maclaurin series for the function.
- 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.
- 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
- 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
- Use the difference of consecutive terms to show that a sequence is
strictly montonic. Look at problems 10.3.1-6
- Use the ratio of consecutive terms to show that a sequence is strictly
montonic. Look at problems 10.3.7-12
- 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 |