## Math 122 Study Guide - Final Exam

1. Solve a first order differential, initial value, problem. Look at 7.7.13 - 7.7.18
2. Find the derivative of the f-inverse. Look at 7.4.30 - 7.7.36.
3. Find the area or volume involving inverse trigonometric functions. Look at 8.2.35 - 8.3.39.
4. Find the volume of revolution. Look at 9.2.43b, 9.2.45 - 9.2.46. Use integration by parts.
5. Find the arc length of a curve, surface area of revolution, or volume of revolution. Look at 9.5.33 - 9.5.36. Use a trigonometric substitution.
6. Solve a differential equation using partial fractions. Look at 9.6.50 - 9.6.53.
7. Find the Laplacian transform for the given function. Look at 10.1.59 - 10.1.62.
8. Work with the Gamma function. Look at 10.3.68.
9. Rotate the coordinate axes to remove the xy-term. Then name the conic and sketch its graph. Look at 12.5.3 - 12.5.8.
10. Find a Maclaurian series for the given function. Give the first four terms of the series and specify the interval on which the series converges to the function. Look at 11.10.40 - 11.10.50.

### Notes:

• All problems are directly from the textbook. They may be odd or even, but the majority of them are even.
• The test is open notebook. You may have old tests, notes, homework, and tables from the book in your notebook.
• You may not use your text book during the test. The problems have been chosen so there should be no need for integration tables.
• Show all work.
• You may use your calculator, but you must show all work. Problems on this test have been picked to minimize the need for technology, but they have also been picked to avoid simple questions which could just be plugged into the TI92 and an answer arrived at.
• The final exam is Tuesday, December 17, from 5:30 to 7:20 pm.