Math 122: Chapter 5 Exam Study Guide

1. Expand the logarithm to be sums, differences, and multiples of simpler logarithms.
2. Rewrite the combination of logarithms as a single logarithm.
3. Find the inverse of the function. Pay attention to restrictions on the domain.
4. Verify that the function has an inverse and then find the derivative of the inverse at the specified point.
5. Use logarithmic differentiation to find the derivative.
6. Find the exact value of the trigonometric function of an inverse trigonometric function. For example, sin(cos^-1 1/3).
7. A slope field for a differential equation is given. Sketch approximate solution curves passing through the indicated points.
8. Find the derivative. 11 parts.
9. Find the integral. 11 parts.

Notes

• Problems are simliar to the book and those covered in class.
• There are 108 points possible, but the maximum you receive is 100 points. Therefore, you may miss 8 points without hurting your grade. Another way to think of this is that you can skip a combination of two derivatives or integrals without adversely affecting your grade.
• You may bring in a piece of paper with the formulas from the derivative section of Theorem 5.20 on page 396.
• You may also write the integrals at the bottom of Theorem 5.20 in inverse hyperbolic trigonometric form (rather than logarithm form) and then use these on the exam.
• Do not write the integration formulas from Theorem 5.20 in logarithmic form on your note sheet.
• You are expected to know the derivatives and integrals for the inverse trigonometric and may not include those on your notesheet.
• When a problem on the exam can be solved using the notesheet, please use the formula without trying to derive it. You may need to make some u-substitutions to get it into the proper form before the formula applies.

Points per problem

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Last updated January 30, 2011 6:38 PM