# Math 121 - Exam 2 Study Guide

1. Given the sketch of a function, find the limits. Also find the value of the function at certain points and determine if the function is continuous at those points. Thirteen parts. Look at problems 2.1.1-6
2. Given the limits of three functions, find combinations of the limits. Five parts. Look at problem 2.2.1
3. Look at a graph and explain why the function is not continuous at the indicated point. Three parts. Use reasons from the definition 2.5.1, continuity at a point. Look at problems 2.5.1-4
4. Find the indicated limits. Five parts. Look at problems 2.2.3-30
5. Find the indicated limits. Five parts. Look at problems 2.2.3-30
6. Find the indicated infinite limits. Three parts. Look at problems 2.3.7-28, 33-36
7. Find the limit numerically. Look at problems 2.1.13-16.
8. Use the definition of a limit to prove a limit. Look at problems 2.4.21-26, 29-34
9. Find the indicated limits involving trigonometric functions. Four parts. Look at problems 2.6.11-32
10. Find the points of discontinuity, if any, and determine whether the discontinuities are removable. Three parts. Look at problems 2.5.11-22, 29-30

## Notes

• Most problems are similar to those from the textbook.
• In many cases, the instructions will say to find the limit using algebraic techniques and show any necessary work. Going to the calculator and plugging in values approaching the number is not an algebraic technique. If there is any doubt about whether or not work should be shown, then show it. You may not receive full credit on some of the more difficult problems if you just have an answer. You may check yourself using numeric techniques, but be sure to show work if you do that so I don't think that's how you found the answer.

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 Total 13 15 6 15 15 9 3 6 12 6 100