images taken from https://apcentral.collegeboard.org

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What is a Limit?

Types of Problems:

• Can change occur at an instant?
• Defining Limits and Using Limit Notation
• Estimating Limit Values from a Graph
• Estimating Limit Values from Tables

Notes & Handouts

Paul's Online Notes: Limits 

• Notes and Practice with Limits
• Solutions to Notes and Practice 

Video Resources

Professor Leonard Videos

• Intro to Limits
• ​Properties of Limits
• ​Continuity of Functions
• ​​Rates of Change Introduction

My Secret Math Tutor Videos

• Average Rate of Change
• ​Average Rate of Change 2
• ​Average Rate of Change ex 1.
• Average Rate of Change ex. 2
• ​Average Rate of Change application example​

​My Secret Math Tutor Videos

• Limit of a Function
• ​Precise Definition of Limit (delta epsilon)
• Instantaneous Rate of Change Approximation
• Instantaneous Rate of Change ex. 1​
• Instantaneous Rate of Change ex. 2

Digital Resources

Desmos Files

• average rate of change​​
• Using a Table to Verify a Limit​
• Using Table to Find Limits ​
• Using Graph to Find Limits

KHAN Academy

• basics of a limit
• average rate of change

CK 12

• concept of a limit
• average rate of change
• instantaneous rate of change

math is fun

• limits intro
• ​limits at infinity

Group Practice

Group Assignment

• Estimate Limits from a Graph
  • last revised 2018-2019

Partner Assignment 

• Graphing Rational Functions with Desmos  
  • last revised 2018-2019

Individual Practice

Average Rate of Change Worksheets

• KUTA Practice Average Rate of Change
  • YOU TUBE Solutions KUTA Avg Rate of Change​
• ​MATH AIDS Practice Average Rate of Change
• ​ONLINE Math Practice Average Rate of Change
• PDF Average Rate of Change
  • ​PDF Average Rate of Change Solutions

Assessments

Formative Assessment

• Average Rate of Change, Instantaneous Rate of Change, Slopes of Secant and Tangent Lines
  • ​​one of the original versions has a typo (correction made)
  • first given 8-20-19
  • See slideshows below for worked out solutions or download pdf on link below
  • worked out solutions
• Limits of Piecewise Functions
  • last revised 2018-2019 
• Graphing Rational Functions
  • ​solutions version 1
  • solutions version 2
  • solutions version 3
  • link to 2018-2019 webpage with how to videos
  • ​​last revised 2018-2019

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Formative Assessment ROC, IROC, slope of secant line, slope of tangent line

Textbook Resources

Rate of Change

• FDWK 4th edition
  • 2.1 pp.66 #1-4

Desmos Files​

• Using a Table to Verify a Limit
• ​Rational Function: Linear Denominator
• ​Rational Function: Quadratic Numerator & Linear Denominator
• Rational Function: Linear Numerator Quadratic Denominator

Determination of Limits from a Table

• FDWK 4th edition
  • ​​2.1 pp.66-67 #15-20, 51-54
  • ​Desmos #15
  • Desmos #16
  • ​Desmos #17
  • ​Desmos #18
  • ​Desmos #19
  • ​Desmos #20
• LHE 6th edition 
  • ​1.2 pp.53-54 #1-10
• LHE 8th edition
  • 1.2 pp.54-55 #1-8​ 
  • DESMOS File 1.2 #1-8
  • LHE 8th Edition 1.2 #7 Proof​

Determination of Limits from a Graph

• FDWK 4th edition​​
  • 2.1 pp.66-67 #25-42​​

• Desmos #25
• ​Desmos #26
• ​Desmos #27
• ​Desmos #28
• ​​Desmos #29
• Desmos #30

• Desmos #31
• Desmos #32
• Desmos #33
• Desmos #34
• Desmos #35
• ​Desmos #35b​
• ​​Desmos #36
• ​Desmos #37-40

• ​​​LHE 6th edition 
  • ​​1.2 pp.53-54 #11-20​​
• LHE 8th edition
  • 1.2 pp.54-55 #9-24
  • DESMOS File 1.2 #9-18​

Applications and Theory

• FDWK 4th edition​​
  • 2.1 pp.66-67 #21-24, 42-50
• LHE 6th edition 
  • ​​1.2 pp.53-54  #1, 21-52​​
• LHE 8th edition
  • 1.2 pp.54-55 #25-74

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Using Algebra and Algebraic Methods to Determine Limits

Types of Problems:

• Determining Limits using Algebraic Properties of Limits​
• Determining Limits using Algebraic Manipulation
• Selecting Procedures for Determining Limits
• Determining Limits using Squeeze Theorem
  

Notes & Handouts

Paul's Online Notes: Limits 

• Notes and Practice with Limits
• Solutions to Notes and Practice 

Video Resources

Professor Leonard Videos

• ​Properties of Limits​​

​Digital Resources

Desmos Files

KHAN Academy

• limit properties

CK 12

• limit properties

Group Practice

Individual Practice

Assessments

Textbook Resources

Determination of Limit using Limit Properties

• FDWK 4th edition
  • 2.1 pp.66-68 #7-14,55-64

Use of the Squeeze Theorem 

• FDWK 4th edition
  
  • 2.1 pp.66-68 #65-68

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Connecting Multiple Representations of Limits

​Types of Problems:

• Connecting a Graph to a Table and Table to Algebra
• Connecting the algebraic methods to the spatial methods of determining a limit

​Notes & Handouts

​Video Resources

​​Digital Resources

Group Practice

​Individual Practice

​Assessments

​Textbook Resources

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Continuity

​Types of Problems:

• Exploring Types of Discontinuity​
• Defining Continuity at a Point
• Confirming Continuity over an Interval
• Removing Discontinuities

​Notes & Handouts

​Video Resources

Professor Leonard Videos

• ​Continuity of Functions

​Digital Resources

Desmos Files

KHAN Academy 

• continuity of a function
• types of ​discontinuity

CK 12

• continuity of a function
• continuity of a function 2

Math is fun

• continuous function

Group ​Practice

​Individual Practice

​Assessments

​Textbook Resources

Different types of discontinuity

• FDWK 4th edition
  • 2.3 pp. 84-86 #1-24

Finding specific values that will guarantee continuity

• FDWK 4th edition
  • 2.3 pp. 84-86 #25-30, 47-50

Verification of Continuity

• FDWK 4th edition
  • 2.3 pp. 84-86 #31-40

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Connection between Asymptotes and Limits

​​Types of Problems:

• ​​Connecting Infinite Limits and Vertical Asymptotes
• ​​Connecting Limits at Infinity and Horizontal Asymptotes

​​Notes & Handouts

​Group Practice

​Individual Practice

​Digital Resources

Desmos Files

KHAN Academy

CK 12

math is fun

• limits and infinity

​Assessments

Textbook Resources

Limits as x approaches a specific value of x

• FDWK 4th edition
  • 2.2 pp. 76-77 #13-20, #27-34

Limit as x approaches positive or negative infinity

• FDWK 4th edition
  • 2.2 pp. 76-77 #1-12, #21-26

End Behavior Models

• ​​FDWK 4th edition
  • 2.2 pp. 76-77 #39-56

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Intermediate Value Theorem

​​Types of Problems:

• Using the Intermediate Value Theorem in different contexts​

​​Notes & Handouts

​Digital Resources

Desmos Files

• intermediate value theorem

Desmos Class Activities
(these require a computer or tablet)

• IVT Activity

KHAN Academy

• intermediate value theorem

CK 12

• intermediate value theorem

Math is Fun

• intermediate value theorem

​Group Practice

​Individual Practice

​Assessments

Textbook Resources

Using IVT 

• FDWK 4th edition
  • 2.3 pp. 84-86 #45,46

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Additional Resources

Professor Leonard's You Tube Channel ​

Paul's Online Notes for Calc 1

Overview of Topics

KHAN Academy: Limits

​​CK 12 Link: Limits

math is fun: Calculus

Libre Texts Online Calculus Books

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