| Section | Topics |
|---|---|
| 5.1, 5.2 | Refer to the list of review topics from our previous exam. |
| 5.3 | Arc length formula for the graph of a function y(x). |
| Arc length formula for parametric (plane) curves. | |
| Exercises | 3-6, 9, any of 11-16. |
| 5.4 | Pumping liquids from containers. |
| Examples 6, 7. | |
| Exercises | 17-19, 35. |
| 5.5 | Fluid force against a vertical plate. |
| Examples 2, 3. | |
| Exercises | 1, 2, 5, 6, 11. |
| 5.6 |
Moment M0 , mass M , and center of mass M0 / M
of a strip along an axis with given density function. |
| Examples 1, 2. | |
| Exercises | 1, any of 5-12. |
| 6.1 | The natural logarithm, its domain, range, and derivative. |
| Laws of logarithms. | |
| Logarithmic differentiation. | |
| Logarithms with general bases (other than e). | |
| Exercises | Any of 1-66. |
| 6.2 | The derivative rule for inverse functions. |
| Inverse equations for ex and ln(x). | |
| Definition of e as a limit. | |
|
General exponential functions (with bases other than e),
their derivatives and anti-derivatives. |
|
| Exercises | 15-18, 41-44, 45-50, 51-58. |
| 6.3 | Derivatives of the inverse trigonometric functions. |
| Examples 7-9. | |
| Exercises | 1, 2, 7-10, 13, 14, 18, 19, 21-26, 27-30. |
| 6.7 | Definitions of odd and even functions. |
| Definitions of the basic hyperbolic functions. | |
| Derivatives of sinh, cosh, and tanh. | |
| Closed formulas for sinh-1, cosh-1, and tanh-1. | |
| Exercises | 5-10, 61-63. |
| 7.1 | As discussed in class on Friday, 11/18/2005. |