# Math 121 - Final Exam Study Guide

1. Use the table to simplify the expressions. Three parts.
2. Consider a triangle with the sin, cos, and tan of three angles given in terms of a, b, and c. Use that information to express the stated quantities in terms of a, b, and c. Two 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. Six 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. Use the table to evaluate and simplify the derivatives. Six parts.
8. Find and simplify the derivatives of the algebraic functions. Four parts.
9. Find and simplify the derivatives of the trigonometric functions. Two parts.
10. Find dy/dx by implicit differentiation.
11. 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.
12. 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.
13. Find all absolute extrema, if any, on the stated interval.
14. Sketch a continuous function based off the sign charts.
15. Express the limit as a definite integral.
17. Write the sum in sigma notation. Do not evaluate.
18. Evaluate the integral with algebraic integrands. Four parts.
19. Evaluate the integral with trigonometric integrands. Two parts.
20. Use the areas in the figure to evaluate the integrals. Three parts.
21. Sketch the region enclosed by the curves and find its area.
22. Sketch the region enclosed by the curves and find the volume of the solid generated when it is rotated about an axis.
23. Find the exact arc length of the curve on the interval.
24. Find the work required to stretch a spring.

## Notes:

• Problems are similar to problems off of old tests in most cases. I looked at the old tests when making up the final.
• 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.