Math 122: Chapter 5 Exam Study Guide

1. Use logarithmic differentiation to find the derivative.
2. Verify that the function has an inverse and then find the inverse of the function. Pay attention to restrictions on the domain.
3. Find the derivative of the inverse at the specified point.
4. Find the equation of the tangent line to the graph of the function at the indicated point.
5. Find the exact value of the trigonometric function of an inverse trigonometric function. For example, sin(cos-1 1/3).
6. Solve the logarithmic and exponential equations for x. Give the exact value.
7. Find the derivative. 12 parts.
8. Find the integral. 12 parts.

Notes

• Problems are simliar to the book and those covered in class.
• You may bring in a piece of paper with derivatives and integrals involving inverse hyperbolic trigonometric functions. These are essentiatlly the formulas from the derivative section of Theorem 5.20 on page 396. You will need the integrals from this theorem as well, but do not use the logarithmic form that is given in the book. Instead rewrite them using inverse hyperbolic trig functions.
• You are expected to know the derivatives and integrals for the inverse trigonometric and may not include those on your notesheet. You are also expected to know the derivatives and basic integrals of the hyperbolic trigonometric functions.
• 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

 # Pts 1 2 3 4 5 6 7 8 Total 4 4 4 4 4 8 36 36 100