# Math 190: Study Guide - Final Exam

1. The graph of a function is given. Use it to find the limits. Seven parts.
2. Complete the table to numerically evaluate the limit.
3. Evaluate the limits. Eight parts.
4. A table with values for x, f, g, f', and g' are given. Use the table to find the derivatives. Eight parts.
5. Find the derivative of the function. Thirteen parts.
6. Evaluate the integral. Nine parts.
7. Given the values of some definite integrals, find the values of other definite integrals. Four parts.
8. Use integration by parts to find the integral.
9. Evaluate a multi-variable function and find the first partial derivatives.
10. The graph of a function and its derivative are shown. Determine which is the function and which is the derivative. Three parts.
11. Find the second derivatives. Two parts.
12. Sketch a function with the given characteristics.
13. Information about a continuous function with exactly one critical point is given. Determine whether that critical point corresponds to a relative minimum, relative maximum, neither, both, not enough information was given, or the situation is impossible. Seven parts.
14. A function and its derivatives are given in factored form. Make sign charts for the function and its derivatives. Determine the x-intercepts, relative maximums, relative minimums, and inflection points. Give the intervals where the function is increasing, decreasing, concave up, and concave down.
15. Find the absolute maximum and minimum of the function on the closed interval.

## Notes

• The test is open notebook. Make sure that your notes are complete in the sections covered on the exam.
• Most of the questions are like those off of previous exams. It is adviseable to go through your old exams and find similar problems and make sure you have them corrected.
• People have a tendency to slow down when they have their notes available to them. They forget that they know anything and think they have to look everything up. That causes them to take much longer than they should. Therefore, you may only use your notes for one hour. Answer as much of the exam as you can without your notes. When you have exhausted your ability from memory alone, then you may notify the instructor, get out your notes, and continue working with your notes. Once an hour is up, you must turn in your test.
• Since your time with your notes is limited, it would be wise to organize your notes ahead of time. Take this study guide and make a note of similar sections in the homework, notes, or old tests that you should look at for help. Then use post-it notes or adhesive tabs to label the sections so that they're easy to find.
• Your notes may consist of homework, handouts, old tests, mathematical notations, etc. You may not use your textbook.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 14 4 21 16 39 36 8 5 9 6 6 6 14 11 5 100