## Math 122 - Chapter 8 Study Guide

1. Sketch the region enclosed by the curves and find its area. Look at problems 8.1.7-22
2. Work application problem involving springs. Look at problems 8.6.4-7
3. Sketch the region and find the volume of the solid that results when the region enclosed by the given curves is rotated about the indicated axis. You're free to choose any of the three methods (disk, washers, or cylindrical shells), but you must use each method at least once. Identify which method you're using. Four parts. Look at problems 8.2.5-22, 8.3.5-16
4. Find the exact arc length of the curve over the given interval. Look at problems 8.4.3-8.
5. Find the exact arc length of the curve over the given interval without eliminating the parameter. Look at problems 8.4.9-14
6. Find the area of the surface generated by revolving the given curve about the indicated axis. Look at problems 8.5.1-16
7. Fluid force problem. Look at problems 8.7.3-8
8. Find the derivative of the hyperbolic trigonometric functions. Two parts. Look at problems 8.8.9-28.
9. Evaluate the integrals involving hyperbolic trigonometric functions. Two parts. Look at problems 8.8.31-46.

### Notes:

• Problems are similar to those in the text.
• You may place the formulas in theorem 8.8.4 on page 506 onto a notecard. You won't need them for the exam, but you may place them on a note card.
 # 1 2 3 4 5 6 7 8 9 Total Pts 8 8 28 8 8 8 8 12 12 100