## Section 10.3 - More Limits

**Essential Question(s):**

Explain how to determine if a limit exists.

Assuming the limit exists, explain the methods you could use to determine the limit of a given function.

How does infinity play a role with limits?

**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.

__A Little History__

- Read this section for enrichment. :) (pg 813)

__Defining a Limit Informally__

- Review the informal definition of a limit at a. (pg 813)
- How can you find a limit of a function? (Ex 1 pg 814)

__Properties of Limits__

- What are the properties of limits? (pg 815)
- How can you use the properties of limits? (Ex 2 pg 815-816)

__Limits of Continuous Functions__

- Review continuity. (pg 90 - 92; also pg 816 small paragraph)
- How do you find the limits using substitution? (Ex 3 pg 816-817)
*(read the paragraph after)*

__One-Sided and Two-Sided Limits__

- What is the left-hand and right-hand limit? (pg 817)
- How do you find the left- and right-hand limits? (Ex 4 pg 817)
- What is a two-sided limit? (top pg 818)
- What is the One-sided and Two-sided limits theorem? (top pg 818)
*(read the paragraph after)* - How do you find the limit at a point of discontinuity? (Ex 5 pg 818)
- How do you find one-sided and two-sided limits? (Ex 6 pg 818-819)

__Limits Involving Infinity__

- What is the definition of a limit at infinity? (pg 819)
- What happens when the limit at infinity isn't a real number? (bottom of pg 819)
- What is an infinite limit and why isn't it considered a limit? (bottom of pg 819 & left)
- How are graphs used to determine limits as x approaches +- infinity? (Ex 7 pg 820)
*(read the paragraph after)* - How are tables used to determine limits as x approaches +- infinity? (Ex 8 pg 820)
- How do you analyze unbounded limits? (Ex 9 pg 821)
- How do you analyze limits at discontinuities? (Ex 10 pg 821)

**STEP 3: Reading**

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

- Read pages 813 - 821.
- Make sure to read the paragraphs between the examples.