Section 10.1 - Limits & Motion: The Tangent Problem

Essential Question(s): 

Explain the distinction between an average velocity and an instantaneous velocity.

---

---

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 Velocity

1. What is average velocity? (pg 792)
2. How do you compute average velocity? (Ex 1 pg 792)

Instantaneous Velocity

1. What is instantaneous velocity? (pg 792 - 793)
   

Limits Revisited

1. What is the informal definition of a limit at a? (pg 794 & read paragraph above box)
   
2. How do you use limits for instantaneous velocity? (Ex 2 pg 794)

The Connection to Tangent Lines

1. Why was a tangent line introduced when finding instantaneous velocity? (pg 795)
2. How do you find the slope of a tangent line? (Ex 3 pg 796)

The Derivative

1. What is the definition of the average rate of change? (pg 796)
2. What is the definition of the derivative at a point? (pg 797)
3. What is another version of the definition of the derivative at a point? (pg 797)
4. When can the derivative not exist? (bottom of pg 797; graphs)
5. How do you find the derivative at a point? (Ex 4 pg 798)
6. What is the definition of the derivative of a function? (pg 798)
7. What is Leibniz notation? (pg 798)
8. How do you find the derivative of a function? (Ex 5 pg 798)-799)

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

• Read pages 792 - 799.
• Make sure to read the paragraphs between the examples.

---

Speed vs Velocity

Continuous Function

Introduction to Calculus

Derivative Introduction

Derivatives as dy/dx

Integration Introduction

Limits

Limits to Infinity

Evaluating Limits