# Math 122 - Chapter 10 Study Guide

- Use any method to determine whether the series converges or diverges. Indicate the method used. Five parts.
- 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.
- 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.
- Differentiate and integrate a power series, leaving the answer in power
series notation.
- Find the radius and intervals of convergence. Three parts.
- 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.
- Manipulate a known Maclaurin series to find the series for a product or quotient.
- Use a Taylor series to approximate a value.
- Solve the initial value problem. It is a 2nd order homogeneous linear differential equation with constant coefficients.
- Use the indicated method to rewrite the integral. Do not integrate. Look back at the techniques in sections 8.2 - 8.5.
- Use Euler's method to solve the differential equation.
- Write the series in sigma notation and determine if it converges. You may find the
College Algebra lecture notes on sequences and series useful.
- Differentiate. Three parts.
- Integrate. Two parts.
- 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

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

Pts |
30 |
10 |
10 |
8 |
18 |
15 |
5 |
7 |
7 |
15 |
5 |
10 |
15 |
10 |
10 |
175 |