Math 122: Chapter 7 Study Guide

1. Find a formula for the derivative of the inverse of a function. Look at problems 7.3.7-10.
2. Solve the logarithmic or exponential equation for x. Two parts. Look at problems 7.1.16-33.
3. 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.
4. Find the derivatives. Eight parts. These could include logarithmic, exponential, inverse trigonometric, hyperbolic trigonometric, or inverse hyperbolic trigonometric functions.
5. Find the derivative of an integral using the second part of the fundmental theorem of calculus. Look at problems 7.6.15-22.
6. Use logarithmic differentiation to find the derivative. Look at problems 7.2.31-34
7. Find the limit. Two parts. Look at problems 7.5.5-34.
8. 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.
9. Find the limit by making substitutions into the limit definition of e. Look at problems 7.6.11-12.
10. Integrate. Five parts. These could include logarithmic, exponential, inverse trigonometric, hyperbolic trigonometric, or inverse hyperbolic trigonometric functions.
11. 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.
12. 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

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 3 6 4 24 3 3 6 12 3 20 12 4 100