Learning Outcomes

1. Use the limit laws to evaluate the limit of a function
2. Evaluate the limit of a function by factoring or by using conjugates
3. Evaluate the limit of a piecewise-defined function

Textbook

• Chapter 2.3  The Limit Laws

Textbook Assignment

• p. 176:    83-101 odd

WeBWorK Assginment

• Limits-Analytic
• Limits-One-Sided
• Limits-Limit Properties

Exit problems of the session

1. Evaluate the limit of 2. Assuming that , , evaluate Key Concepts

• The limit laws allow us to evaluate limits of functions without having to go through step-by-step processes each time.
• You can evaluate the limit of a function by factoring and canceling, by multiplying by a conjugate, or by simplifying a complex fraction.

#### Videos and Practice Problems of Selected Topics

• Evaluating limits using limit laws
1. Limit properties (5:07) What is the limit of the sum of two functions? Difference? What about the product? Division? A function rasised to a number?
2. Limits of combined functions (4:08) Given the graphs of and , find . Then, given the graphs of and , find .
3. Limits of combined functions: piecewise functions (4:12) The graphs of two piecewise functions, and , are given. Find , and .
4. * Practice:  Limits of combined functions: sums and differences. (4 problems)
5. * Practice:  Limits of combined functions: products and quotients. (4 problems)
6. Limits of composite functions (5:11) Given the graphs of and , find . Then, given the graphs of other functions and , find . Two more graphs are given for the functions and to find .
7. * Practice: Limits of composite functions. (4 problems)
• Evaluating limits using algebraic manipulations
1. Limits by factoring (5:44) Find .
2. * Practice: Limits by factoring. (4 problems)
3. Limits by rationalizing (9:31) Find .
4. * Practice: Limits using conjugates. (4 problems)