## Section 2.1 - Rates of Change and Limits

**Essential Question(s):**

What are limits and how do you determine if they exist?

**Follow**__these three steps__to complete this "flip" lesson.**STEP 1: Preparation**

__Title__your spiral with the heading above and

__copy__the essential question(s).

**STEP 2: Vocabulary & Examples**

__Copy__and

__define__the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed.

__Review__the following examples and

__copy__what is necessary for you. Use the guiding questions for your cornell notes.

__Average and Instantaneous Speed- REVIEW__

- What are the average rate of change ratios? (pg 59)
- How do you find the average speed? (Ex 1 pg 59)
- What is instantaneous rate of change? (pg 59)
- How do you find instantaneous rate of change? (Ex 2 pg 60)

__Definition of Limit__

- What is the role of a limit? (pg 60 2nd paragraph)
- What do limits never depend on? (pg 60 3rd-5th paragraph & figure)
- What is the limit of sin(x)/x as x approaches 0? (pg 60)

__Properties of Limits__

- What are the properties of limits? (table pg 61-62)
- How do you use the properties of limits (Thm 1)? (Ex 3 pg 62)
- How do you use limits with Polynomial and Rational Functions (Thm 2)? (table page 62)
- How do you use Theorem 2? (Ex 4 g 63)
- How can you use the product rule? (Ex 5 pg 63)
- How can you explore a nonexistent limit? (Ex 6 pg 63)

__One-Side__d a nd T wo-Sided Limit s

- What is a left-hand and right-hand limit? (pg 63)
- How can you find limits of the greatest integer function? (Ex 7 pg 64)
- What is the greatest integer function also know as? (pg 64)
- What is a two-sided limit? (pg 64)
- How do you know if a function has a limit as x approaches a value? (Thm 3 pg 64)
- What if the function isn't defined? (left column pg 64)
- How do you determine right- and left-hand limits? (Ex 8 pg 64)

__Squeeze Theorem__

- What is the purpose of the Squeeze Theorem? (pg 64)
- What is the Squeeze Theorem? (Thm 4 pg 65)
- How do you use the Squeeze Theorem? (Ex 9 pg 65)

**STEP 3: Reading**

__Read__the following page(s) and take any extra notes as needed.

- Read pages 59-65.
- Make sure to read the paragraphs between the examples and sidebar snippets.