Section 10.2 - Limits & Motion: The Area Problem

Essential Question(s): 

Explain how area is used to determine distance traveled from changing velocity.

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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.

Distance from a Constant Velocity

1. Review computing distance traveled? (Ex 1 & Ex 2 pg 804-805)

Distance from a Changing Velocity

1. What is used to determine distance from a changing velocity? (pg 805)
   

Limits at Infinity

1. What is the informal definition of a limit at infinity? (pg 805)
2. Consider the exploration 1. How were limits used? (pg 805-806)

The Connection to Area

1. How is area used to calculate distance of a velocity function that varies? (pg 806)
2. How do you approximate an area with rectangles? (Ex 3 pg 807) ***Make sure to read paragraphs below example***

The Definite Integral

1. How is a summation used with finding area? (top of pg 808)
2. What is a Riemann sum? (left pg 808)
3. What is the definite integral? (pg 808) ***big deal***
4. How can you use area to compute an integral? (Ex 4 & 5 pg 808-809) (read the paragraph prior)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 804 - 809.
• Make sure to read the paragraphs between the examples.

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Speed vs Velocity

Continuous Function

Introduction to Calculus

Derivative Introduction

Derivatives as dy/dx

Integration Introduction

Limits

Limits to Infinity

Evaluating Limits