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MAC2233  -  Business Calculus I
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Notes for Regular Calculus
     
Chapter 1


SLOPE of a line -  Notes

The Difference Quotient -  Notes-Theory
The Difference Quotient -  Example: f(x) = x3

Line tangent to a curve at a point - Notes
Changing slope of a curve - animation1 animation2

Estimate the "slope" of a parabola at a point  -  avi


Limits

Finding Limits - Graphically - Worksheet
Limit of a Function, Graphical & Numerical -
Notes (2 pages)
Limit of a Function 1 - Notes (7 pages)Summary
Limits of a Piecewise-Defined Function - Notes (2 pages)
Hiccup Function - Limit -  Notes
(6 pages)  ,  Summary
Limits of a Piecewise-Defined Function 2 -
Worksheet

Finding Limits - Graphically - Worksheet
Properties of Limits - Notes


Continuity
Continuous Functions - Definitions - Informal - Formal
Hiccup Function - Continuity - Notes
Removable and Non-Removable Discontinuities - Worksheet



Limit of the Slope of a Function - Interactive1 Interactive2

Indeterminate Forms - Worksheet



Rational Functions
Polynomials: Definitions, Classify, Properties - Notes

Rational Function with a Hole1 - Notes
Polynomials - End Behavior / Dominant Terms - Notes
Rational Functions and Asymptotes Summary - OutlineAdvanced
Infinite Limits: Do Not Exist - Explanation
Infinite Limits & Notation - Graphs
Special Cases of Rational Functions - Notes



   
Chapter 3
  The Derivative
   

Introduction to the Derivative
Uses of Differential Calculus & Integral Calculus  -  Notes

Fruit fly population - Notes 
(3 pages)
Line tangent to a curve at a point - Notes
Estimate the "slope" of a parabola at a point  -  avi
Changing slope of a curve - animation1 animation2
The slope formula :  Notes

Calculating Derivatives

The derivative of a Function -   Def h & delta xDef XoDef hDef delta x
Left-hand derivative, Graphical & Numerical - Notes
Notations for the derivative - Notes
The Difference Quotient - Ex: f(x) = x^3
The derivative of f(x) = sqrt(2x) - Example

Matching a derivative to its function - worksheet
Draw the derivative from its function - worksheet
Differentiability implies continuity - proof
Derivative Formulas - Formulas1 Formulas2  ,  Formulas3
(2 pages)
Derivative Problems - Worksheet
Higher Order Derivatives - Graph
Derivative of xn - proof
Derivative quotient rule - proof
Derivative of ex - proof

Position & Velocity
Position vs Time (horizontal) - pdfavi GRAPH Animation  (Calc, then Animate)
Anvil Launching Competition:
    The right way  -  YouTube  ,  website

    Something goes wrong -  YouTube  ,  website
    Graphing Position vs. Time (vertical)  -  worksheetanimation-avi
    Secant line vs. tangent line - worksheet
Horizontal Motion (graph of velocity function) - notes
Launching a Rocket - worksheet
Motion along a straight line - Worksheet

Position vs Time s(t)=t^3-6t^2+9t - Notes
Position vs Time (vertical) -  avi
Position vs Velocity - Worksheet & Notes 
(4 pages)

Linearization and the Differential

Find an equation of the tangent line - notes
Tangent Line Approximations -  notes-anotes-Δx , Linearization

Chapter 4
 

The Derivative in Graphing and Applications

Curve Sketching
Curve Sketching - Purpose
Absolute Extreme Values - GRAPH
The Min/Max Thm - Notes

Mean Value Theorem
Mean Value Thm  -  Theorem
Rolle's Thm vs. Mean Value Thm  - graph
Converting Mean Value Thm to Rolle's Thm -  example
Mean Value Thm -  proof
Constant Difference Thm - Notes

Using Derivatives to Analyze Slope and Concavity
Increasing / Decreasing / Constant Functions - Notes
Show the sign of f(x) , f(x) , and f(x) on a number line  -  Notes
Analyze the sign of f(x) , f(x) , and f(x)  -  Worksheet
Relating graphs of f(x) , f(x) , and f(x) -  ex 1ex 2ex 3ex 4

Using slope tables and concavity tables: f(x) = x3-3x+4  -  Example
 
Using graphs of derivatives to analyze f(x) - GRAPH  ,
Sketch f(x) given the graph of its derivative -  WorksheetKey
Using derivatives to analyze f(x) - pdf  (6 pages)

Rectilinear motion - Motion along a line
Rectilinear Motion -  Description
Speeding up / Slowing down  -  Notes
Position vs Time (horizontal):   s(t) = 5t3 - 30t2 + 45t
   Worksheet - Worksheet
   Animation - avi  ,  GRAPH Animation  (Calc, then Animate)
Postion vs Time (horizontal):   s(t) = 3t4 - 16t3 + 18t2
   Worksheet with equation
   Worksheet without equation

Newton's Method
Newton's Method - Example , Theory
Graphical Demonstration - PowerPoint

Maximize the Area of an Inscribed Rectangle - grf animation  ,  extra

Finding e - Proof using Limits & L'Hopital's Rule - Notes

     
Chapter 5
  Integration
    Uses of Differential Calculus & Integral Calculus  -  Notes
Limit of the Area Under a Curve - Notes
Limit of the Area Between Two Curves -
Notes
Chapter Notes  -  Chapter 5

Constant Difference Thm - Notes
Estimate the Area Under a Curve -  NotesC , NotesBW
Estimate the Area Under a Curve -  Numerical Techniques
(2 pages)
Area under a Curve -  Summation  ,  Infinite Sum
Motion along a straight line - Worksheet
The Definite Integral -  Vocabulary
The Fundamental Theorem of Calculus -  Notes
2nd Fundamental Theorem of Calculus -  Worksheet
Estimate the Area Between Two Curves - Limits 1 - Notes1Notes2
Average Value of a Function - Notes
Mean Value Theorem for Integrals - Notes

Formulas
Geometry Formulas -  Formulas
Differentiation / Integral Formulas:  Formulas3 (2 pages) , Formulas2  , Formulas1 - Large
Summary of Integral Applications - Formulas