# Math 122: Chapter 7 Study Guide

- Find a formula for the derivative of the inverse of a function. Look at
problems 7.3.7-10.
- Solve the logarithmic or exponential equation for x. Two parts. Look at problems 7.1.16-33.
- Find the derivative of one of the inverse trigonometric functions by using
an appropriate triangle and the derivative of a trigonometric function. Look
at pages 490-493 and your lecture notes.
- Find the derivatives. Eight parts. These could include logarithmic, exponential, inverse trigonometric, hyperbolic trigonometric, or inverse hyperbolic trigonometric functions.
- Find the derivative of an integral using the second part of the fundmental
theorem of calculus. Look at problems 7.6.15-22.
- Use logarithmic differentiation to find the derivative. Look at problems
7.2.31-34
- Find the limit. Two parts. Look at problems 7.5.5-34.
- Find the limit. Four parts. Look at problems 7.5.5-34. This is the same as #7, it's just split across two pages to give you more room to work the problems.
- Find the limit by making substitutions into the limit definition of e. Look at problems 7.6.11-12.
- Integrate. Five parts. These could include logarithmic, exponential, inverse trigonometric, hyperbolic trigonometric, or inverse hyperbolic trigonometric functions.
- Integrate. Give exact answers when there are definite integrals. Three parts. These could include logarithmic, exponential, inverse trigonometric, hyperbolic trigonometric, or inverse hyperbolic trigonometric functions. This is the same as #10, just split because it takes more than one page.
- Use calculus to find the absolute extrema and inflection points on a closed interval. Look at problems 7.4.5-8 and 7.4.30, 31, 33.

## Notes

- Show work!
- You may create notecards that have the following formulas on them.
- Integrals resulting in an inverse trigonometric function (page 494)
- Derivatives of the inverse hyperbolic trigonometric functions (page
505)
- Integrals resulting in an inverse hyperbolic trigonometric function
(page 506). Do not use the equivalent logarithmic form.

- You are expected to know the derivatives of the inverse trigonometric functions.
- You are expected to know the derivatives of the trigonometric and hyperbolic
trigonometric functions.

## Points per problem

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

Pts |
3 |
6 |
4 |
24 |
3 |
3 |
6 |
12 |
3 |
20 |
12 |
4 |
100 |