# Math 121: Chapter 1 Exam Study Guide

1. Use the graph of y = f(x) to find the indicated values. These may include one-sided and two-sided limits, the value of a function, and points of discontinuity. 8 parts.
2. Use the graph of y = f(x) to find the indicated values. These may include one-sided and two-sided limits, the value of a function, and points of discontinuity. 6 parts.
3. Use your calculator to approximate the limit numerically. You do not have to make a table like the problems in the text. Make sure your calculator is in radian mode. 3 parts.
4. Find the limit. Many/most of these can be done without showing work. 16 parts.
5. Determine where there are any discontinuties and whether they are removable or non-removable. 2 parts.
6. Find the limit and show work (even if you can do it without showing work). I will be grading the work on these. Be sure to write the "lim" until you actually find the limit. Also make sure your work is correct; don't do illegal things like squaring an expression or taking the square root of each term of a sum. 5 parts.
7. Use the ε-δ definition to prove a limit. The definition is not given on the exam, you need to know what it is. Also note that this is not going to be finding the limit of a linear expression, so be sure to focus on those involving picking an arbitrary δ.

## Notes

• Be sure that when you're showing work, you continue to write the limit symbol until you actually find the limit.
• Most of the problems are similar to those in the textbook.
• This is a skills test; there aren't any deep conceptual or story problems on it.
• There are 106 possible points, so you can miss a few and still come out okay on the exam.
• Remember to go through the exam before you start and identify problems you think you can do easily and which ones are going to give you more difficulty. Work through the easiest (for you) problems that are worth the most amount of points.

## Points per problem

 # Pts 1 2 3 4 5 6 7 Total 8 6 9 48 6 24 5 106