# Math 121 - Exam 3 Study Guide

1. Simplify the limit of the summation. Look at problems 5.4.25-26.
2. Use part 2 of the fundamental theorem of calculus to evaluate the derivative. Look at problems 5.6.43-46. Pay attention to those where the upper limit is a function.
3. Find all critical points of the function and identify them as relative maximums, minimums, or neither.
4. Rewrite the integral in terms of u and change the limits, but do not evaluate.
5. Use the areas shown in the figure to find the definite integrals. Seven parts. Look at problem 5.5.17-18.
6. Find all absolute extrema of the function on the given interval.
7. A velocity and position function are given. Find the displacement and distance on the given time interval.
8. Related rate problem.
9. Evaluate the integrals. They may be indefinite or definite and may or may not require substitutions. Five parts.
10. Solve the initial value problem.
11. Evaluate the limits. Four parts. Show work or justification. An example of justification might be "form 7/0+ → ∞"
12. The value of a trig function and the quadrant the angle lies in is given. Use it to find other trigonometric expressions.
13. A table of values is given. Use it to find the indicated derivatives.
14. The graph of an unknown function is shown along with key points on the curve. Write summations to find the area of a region under the curve, the volume when the region under the curve is rotated about each axis, the length of the curve, the area of the surface generated when the curve is rotated about an axis. Then write summations for rotating about lines other than an axis. Eight parts. Look at problem 6.2.37.
15. Work problem involving springs. Look at problems 6.7.6-11. Work the problem as far as the integral, but do not evaluate. Give the proper units on the answer.
16. Work problem. Look at problems 6.7.12-21. Work the problem as far as the integral, but do not evaluate. Give the proper units on the answer.
17. Find the pressure on a horizontally submerged surface and the fluid force on a vertically submerged surface. Look at problems 6.8.3-8. Work the problem as far as the integral, but do not evaluate. Give the proper units on the answer.

## Notes

• On many of the application problems from chapter 6, the instructions are to setup the integral that is needed to find the answer but to not evaluate it. This will help with the time issue and hopefully avoid arithmetic errors.
• Some of the questions are over previous chapters.

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total 6 6 14 8 21 8 8 8 40 8 24 15 18 32 8 10 16 250