Mr Hickman's Class 2022-2023
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images taken from https://apcentral.collegeboard.org

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

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

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

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


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

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

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

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




Mr Hickman is available for assistance after school practically anytime.  Talk to me to be certain that I am aware you are coming and 99% of the time I will be able to help you