# Math 121 - Final Exam Study Guide

1. Use the table to simplify the expressions. Four parts.
2. Consider two acute angles with a sine, cosine, or tangent for each angle given. Use that information to find the exact value of the expression. Four parts.
3. Use the sketch of the function to find the limits. Also tell whether the function is continuous, differentiable, and integrable at a point or on an interval. Nine parts.
4. Find the limits of algebraic expressions. Show work where necessary. Five parts.
5. Find the limits of trigonometric expressions. Show work where necessary. Two parts.
6. A graph of a function and its derivative are shown. Label the function as f and the derivative as g. Three parts.
7. Find and simplify the derivatives of the trigonometric functions. Two parts.
8. Find dy/dx by implicit differentiation.
9. Find and simplify the derivatives of the algebraic functions. Three parts.
10. Use the table to evaluate and simplify the derivatives. Six parts.
11. Find all absolute extrema, if any, on the stated interval.
12. Sketch a continuous function based off the sign charts.
13. Classify each critical point as a relative maximum, relative minimum, neither, impossible, or not enough information given to determine. Assume that the function is continuous and has only one critical point. Five parts.
14. Determine by inspection whether the function on the interval will have an absolute maximum, absolute minimum, both, neither, or not enough information is given. Four parts.
15. Evaluate the sum.
16. Write the sum in sigma notation. Do not evaluate.
17. Express the limit as a definite integral.
18. Approximate the area under a curve on a given interval by using either left hand endpoints, right hand endpoints, or midpoints (the technique is specified). The x and y coordinates of points are given.
19. Evaluate the integral with algebraic integrands. Three parts.
20. Evaluate the integral with trigonometric integrands. Two parts.
21. Use the areas in the figure to evaluate the integrals. Three parts.
22. Sketch the region enclosed by the curves and find its area.
23. Sketch the region enclosed by the curves and find the volume of the solid generated when it is rotated about an axis.
24. The x and y coordinates of points along a curve are given, use them to approximate the arc length of the curve on the interval.

## Notes

• Problems are similar to problems off of old tests in most cases. I looked at the old tests when making up the final.
• Problems, for the most part, are in chapter order.
• The final exam is open notebook. You may have any notes, homework, handouts, tests, or study guides in your notes. You may not photocopy the book and put it into your notes. You may (and should) go back and reinforce your notes in the areas they're weak.
• You will want to answer as many of the problems as you can without looking at your notes first, otherwise, you will run into time problems finishing this exam.

## Point values per problem

 # Pts # Pts 1 2 3 4 5 6 7 8 9 10 11 12 8 8 18 20 8 9 8 4 12 18 4 4 13 14 15 16 17 18 19 20 21 22 23 24 Total 10 8 4 4 4 5 12 8 9 5 5 5 200