Home  

MAC2311  -  Calculus I
Handouts & Worksheets


Syllabus
Tests
Handouts  
TI-83 Plus
Misc.
Links

 

 

 

Review Handouts and Worksheets

 

Algebra Study Guide - Courtesy of AIMS Community College - Worksheet

 

 

 

Review for Calculus

 

Uses of Differential Calculus & Integral Calculus  -  Notes
The "Rule of Five"  -  Notes
Parent Functions -
Notes
Transformations Outline - Notes
Transformations Summary - Notes
Transformations
Worksheet
Transformations Calculus Review - Class Worksheet
Analyze Functions Review - Class Worksheet
See MAC1105 College Algebra for
Review

Great Symbolic Manipulator - SolveMyMath.com   (perform tedious calculations, etc.)
Best Graphing Program! - GRAPH (for free download)
   
Chapter 2

Limits
Limit of a Function, Graphical & Numerical - Notes (2 pages)
Limit of the Area Under a Curve - Notes
Limit of the Area Between Two Curves -
Notes
Limit of a Function 1 -
Notes (7 pages)Summary
Limits of Piecewise-Defined Functions - Worksheet (2 pages)
Hiccup Function - Limit -  Notes (6 pages)  ,  Summary
(Briggs textbook) Interactive Figures - Holecos(1/x)
Limit of the Slope of a Function - Interactive1 Interactive2
Properties of Limits - Notes

Limits of a Piecewise-Defined Function 2 - Worksheet
Indeterminate Forms - Worksheet

Graph showing lim x -> +inf  sin(x)/x = 0 -  Notes
lim x->0  sin(x)/x = 1  -  GraphProof

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

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


Epsilon/Delta Proof
Informal Epsilon/Delta Example -
Notes
Formal Epsilon/Delta Definition of a Limit -
Notes
Limit of Exponential Function (epsilon/delta) -
Notes
Limit of a Function, Graphical & Numerical - Notes
Limit of a Piecewise-Defined Function -
Notes

   
Chapter 3
  The Derivative
   

Introduction to the Derivative
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)

Trigonometric Functions
Trig Identities & Formulas - Everything
Identities
Trig Functions & Inverse Trig Functions - TrigFcns.grf ,  [ Download GRAPH ]
Inverse Trig Functions - sinx, cosx, tanxcotx, secx, cscx
Transcendental Functions & Derivatives - Summary

Derivative of Inverse Functions Theorem - Notes
Derivative of sin-1(x) - proof

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
    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

Web Sites
Integral Calculator - SolveMyMath.com
Wolfram Alpha - Link
Wolfram Mathematica Online Integrator  -  Link