## Math 190 - Final Exam Study Guide

1. Find the indicated limits. Eight parts.
2. Use the limit definition of the derivative to find the derivative. Show work.
3. Find the equation of a tangent line to a curve at a given point.
4. Use logarithmic differentiation to find the derivative.
5. Find the derivative of the function. Twelve parts.
6. Sketch a function with the given characteristics.
7. Consider a function. Find the intervals where the function is increasing, decreasing, concave up, and concave down. Find any relative extrema and inflection points.
8. Find the absolute maximum and minimum of a function on a closed interval.
9. Application problem. Newton's law of cooling.
10. Evaluate the integral. Ten parts. Some are indefinite, some are definite. Some require u-substitutions, some require integration by parts. Some are improper.
11. Find the first order partial derivatives.
12. Find the second derivatives. Two parts.
13. Find the area of the region between two curves.

### Notes:

• Most of the problems were obtained by looking at previous tests and arriving at similar problems. None of the problems are directly from previous tests. None of the problems are knowingly from the textbook.
• You may use your notebooks on the test. The notebook may contain notes, homework, old tests, and any handouts. It may not contain photocopies of the text, nor may the text be three-hole punched and stuck into your notebook.
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 Tot pts 24 5 5 5 60 5 12 6 5 50 8 10 5 200