# Math 122: Chapter 7 Study Guide

1. Find a formula for the derivative of the inverse of a function. Look at problems 7.1.45-48.
2. Solve the logarithmic equation for x. Look at problems 7.2.16-25.
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 the example on page 494.
4. You are given a graph. Assume the graph is the graph of y=f(x) and determine if f is a one-to-one function. Using the same graph, assume it is the graph of y=f'(x) and determine f is a one-to-one function. Three parts.
5. Find the derivative involving log and exponential functions. Two parts. Look at problems 7.3.1-30.
6. Integration involving log and exponential functions. Two parts. Look at problems 7.3.61-72.
7. Find the derivative and integral of a hyperbolic trig function. Look at problems 7.8.9-18, 31-38.
8. Find the derivative of an integral using the second part of the fundmental theorem of calculus. Look at problems 7.5.15-16, 21-22.
9. Show the form of the limit and then evaluate the limit using L'Hôpital's rule. Three parts. Look at problems 7.7.3-36.
10. Find the derivative. Four parts. Look at problems 7.3.1-30 and 7.6.23-30.
11. Use logarithmic differentiation to find the derivative. Look at problems 7.3.35-45.
12. Use calculus to find the coordinates of the absolute maximum and minimum of the continuous function on the closed interval. Remember from Calculus 1 that absolute extrema can occur at critical points or at end points. Look at problems 7.4.5-14.
13. Integrate. Give exact answers when there are definite integrals. Three parts. Look at problems 7.6.33-46 and 7.8.39-49
14. Find the limit. Show work or justification. Three parts. Look at problems 7.7.3-36.

## Notes

• Problems 1-9 must be worked without a calculator or computer and turned in before the rest of the exam may be started. You may not come back and rework these problems the second day of the test. You may not use your notecards on this part of the test.
• Problems 10-14 can be checked with a calculator or computer, but work must be shown. This part may be started only after the first portion of the exam is completed. You may use your notecards on this part of the test.
• You may create notecards that have the following formulas on them.
• Integrals resulting in an inverse trigonometric function (page 496)
• Derivatives of the inverse hyperbolic trigonometric functions (page 516)
• Integrals resulting in an inverse hyperbolic trigonometric function (page 517). 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 13 14 Total 4 4 4 6 8 8 6 4 12 12 4 4 12 12 100