Learning Outcomes

1. Use tables to estimate the limit of a function or to identify when the limit does not exist
2. Use graphs to estimate the limit of a function or to identify when the limit does not exist
3. One-sided and two-sided limits and their relationship

Textbook

• Chapter 2.2  The limit of a Function

Textbook Assignment

• p. 154:   30-33 all, 35, 38, 42

WeBWorK Assginment

• Limits-Introduction

Exit problems of the session

1. Use a table to estimate the limit of .
2. Use a graph to estimate limits: Textbook pp. 157: 59-64

Key Concepts

• A table of values or graph may be used to estimate a limit.
• If the limit of a function at a point does not exist, it is still possible that the limits from the left and right at that point may exist.
• If the limits of a function from the left and right exist and are equal, then the limit of the function is that common value.
• We may use limits to describe infinite behavior of a function at a point.

#### Videos and Practice Problems of Selected Topics

• Estimating the limit using graphs
1. Estimating limit values from graphs (6:00) Two graphs are given. Find , and , , and .
2. Unbounded limits (2:31) A discussion on and using graphs.
3. One-sided limits (9:10) Three graphs are given and several one-sided limits are estimated.
4. * Practice: Analyze the graph of a function to find the limit. (5 problems with a guiding text)
5. * Practice: Estimating limit values from graphs. (6 problems with a guiding text)
6. * Practice: Estimating limit values from graphs. (4 problems)
7. * Practice: One-sided limits. (4 problems)
• Estimating the limit using tables
1. Approximating limits using tables (4:26) Use tables to estimate .
2. Estimating tables from limits (3:23) Selected values of are given to estimate .
3. * Practice: Using tables to approximate limit values. (5 problems with a guiding text)
4. * Practice: Creating tables for approximating limits. (4 problems)