Learning Outcomes

- Use the limit laws to evaluate the limit of a function
- Evaluate the limit of a function by factoring or by using conjugates
- 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 **

- Evaluate the limit of
- 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
, by*factoring and canceling*, or by*multiplying by a conjugate*.*simplifying a complex fraction*

#### Videos and Practice Problems of Selected Topics

**Evaluating limits using limit laws**

- 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?
- Limits of combined functions (4:08) Given the graphs of and , find . Then, given the graphs of and , find .
- Limits of combined functions: piecewise functions (4:12) The graphs of two piecewise functions, and , are given. Find , and .
- * Practice: Limits of combined functions: sums and differences. (4 problems)
- * Practice: Limits of combined functions: products and quotients. (4 problems)
- 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 .
- * Practice: Limits of composite functions. (4 problems)

**Evaluating limits using algebraic manipulations**

- Limits by factoring (5:44) Find .
- * Practice: Limits by factoring. (4 problems)
- Limits by rationalizing (9:31) Find .
- * Practice: Limits using conjugates. (4 problems)