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. Given a graph of a function, determine whether or not the function is one-to-one. Some of the graphs may be of f and some may be of f'. Three parts.
5. Find the derivative. Two parts. Look at problems 7.3.1-30.
6. Integrate. 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. Look at problems 7.5.15-16, 21-22.
9. Find the limit. Two parts. Look at problem 7.7.49.
10. Find the limit using L'Hôpital's rule. Two parts. Look at problems 7.7.3-36.
11. Find the derivative. Four parts. Look at problems 7.3.1-30 and 7.6.23-30.
12. Use logarithmic differentiation to find the derivative. Look at problems 7.3.35-45.
13. Use calculus to find the coordinates of the extrema and inflection points. Look at problems 7.4.5-14.
14. Integrate. Give exact answers when there are definite integrals. Three parts. Look at problems 7.6.33-46 and 7.8.39-49
15. Find the limit. Show work or justification. Three parts. Look at problems 7.7.3-36.

Notes

• The exam is scheduled for 1.5 days.
• Problems 1-10 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. This portion is 52% of your test.
• Problems 11-15 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. This portion may be continued on the second day of the exam, the instructor will not grade any of the second part until after the second day of the exam. You may use your notecards on this part of the test. This portion is 48% of your 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

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Last updated September 4, 2003 7:42 PM