hàm liên tục

Tim Brzezinski, Đoàn Ngọc Lê, Sep 10, 2017

[b][color=#1551b5]This GeoGebra book contains applets that can be used to foster active, student-centered, discovery-based learning, provide meaningful remediation, enhance opportunities for differentiation of instruction, and serve as a source of ongoing formative assessment. [/color] [color=#0a971e]These GeoGebra books display the amazing work from several esteemed members of the GeoGebra community. I am truly humbled and amazed by their talents. These comprehensive resources would not have been possible without their contributions. I would like to express a BIG THANK YOU to Steve Phelps ([url]https://www.geogebra.org/stevephelps[/url]) Dr. Ted Coe ([url]https://www.geogebra.org/tedcoe[/url]) Kevin Hopkins ([url]https://www.geogebra.org/dochopatsbu[/url]) John Golden ([url]https://www.geogebra.org/goldenj[/url]) Irena Boyadzhiev ([url]https://www.geogebra.org/irinaboyadzhiev[/url]) Terry Lee Lindenmuth ([url]https://www.geogebra.org/tlindy[/url]) Doug Kuhlmann ([url]https://www.geogebra.org/dkuhlmann[/url]) rockyroer_1 ([url]https://www.geogebra.org/rockyroer_1[/url]) [/color] [color=#1551b5]More dynamic worksheets will continue to be added to this volume over time. [/color] [color=#444]Teachers: [/color] [color=#b20ea8]It is my hope that these resources help empower your students to actively (and meaningfully) discover these calculus concepts. [/color] [color=#444]Students:[/color] [color=#b20ea8]It is my hope that these resources help you discover & help reinforce these calculus concepts in a way that makes sense to you. [/color] [color=#1551b5]For questions, suggestions, and/or comments, feel free to e-mail me at any time. I wish you much success in your journey of teaching and/or learning mathematics! [/color] [color=#0a971e]Best, Tim Brzezinski ([url]www.geogebra.org/tbrzezinski[/url]) Independent Mathematics Education Consultant Adjunct Instructor of Mathematical Sciences (Central Connecticut State University) E-Mail: dynamicmathsolutions@gmail.com Twitter: @dynamic_math ([url]https://twitter.com/dynamic_math[/url]) [/color] [/b]

Table of Contents

  1. Preliminary Review Topics
    1. Pythagorean Trigonometric Identity (1)
    2. Trig ID Movie (II)
    3. Trig ID Movie (III)
    4. Exponential Functions: Graphs
    5. Logarithmic Functions: Graphs
    6. Logarithmic Action!
    7. Logarithmic Action (2)!
    8. Logarithmic Action (3)!
    9. Logarithmic Action (4)!
  2. Limits & Continuity
    1. Limits: Introductory Questions
    2. One CRAZY Limit !!!
    3. CRAZY FUNCTION!!!
    4. A tool to explore delta-epsilon understandings.
    5. Cont in uity
    6. IVT Dynamic Illustrator
    7. Continuity Questions
    8. Vertical Asymptote (Defined as a Limit)
    9. Horizontal Asymptote (Defined as a Limit)
    10. One Special Limit
  3. Derivatives: Introduction & Intuition
    1. Average Velocity
    2. Average to Instantaneous (Intro)
    3. Sketch the Derivative (Warm Up)
    4. Drawing Derivatives
    5. Constructing Graphs of Derivative Functions (Intuitively)
    6. Average Rate of Change Intervals
    7. Average Rate of Change of a Function: Dynamic Illustration
    8. Average Rate of Change vs. Instantaneous Rate of Change
    9. Derivatives (Intro)-1
    10. Derivatives (Intro)-2
    11. Graphing The Derivative of a Function
    12. 3-Way Color-Changing Derivative Grapher
    13. When does f'(x) = f(x)?
    14. Mean Value Theorem
    15. Mean Value Theorem (Without Words)
  4. Derivatives of Special Functions & Differentiation Techniques
    1. Derivative of a Product
    2. Important Trig Limits
    3. Derivative of Sine & Cosine Functions (Quick Investigation)
    4. Derivative of Tangent Function (Investigation)
    5. Implicit Differentiation: Intro
    6. Folium of Descartes
    7. Implicit Differentiation (Quick Check)
    8. Derivative of Arcsine Function
    9. Derivative of Arccosine Function
    10. Derivative of Arctangent Function
    11. Derivatives of Inverse Functions
    12. Derivative of Natural Log Function
  5. Related Rates & Linearization of Functions
    1. Related Rates (1)
    2. Related Rates (2)
    3. Falling Ladder !!!
    4. Related Rates (3)
    5. Related Rates: Adjustable Cone with dh/dt Constant
    6. Related Rates (Rolling Carts Problem)
    7. Linearization Illustrator (Calculus)
    8. Linearization Checker (Calculus)
    9. Newton's Method: Illustrated
  6. Closed Interval Method & Optimization Problems
    1. Critical Numbers & Critical Points of Functions (Intro)
    2. The Closed Interval Method (Application Problem)
    3. Optimization: Area of a Rectangle
    4. Minimizing the Area of a Triangle
    5. Optimization - Box
    6. Maximizing Trapezoid Area
    7. Optimization Challenge 1
    8. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
    9. Honeybee Population (Growth Rate Question)
    10. Oil Pipeline Optimization Problem
    11. Cylinder Inscribed Inside Sphere
    12. Cylinder Inscribed In Cone
    13. Distance From Point to Graph
    14. Optimization Problem: Isosceles Triangle Circumscribed about a Circle
  7. Riemann Sums; Indefinite and Definite Integrals
    1. Definite Integral Illustrator (I)
    2. Trapezoid: Area (I)
    3. Definite Integral Illustrator (II)
    4. Definite Integrals: Sum
    5. What Makes a Function Even?
    6. What Makes a Function Odd?
    7. Odd Functions: Another Look (Take 2)!
    8. Accumulations
    9. All Sums (Riemann Sums)
  8. Areas and Volumes; Solids of Revolution & Non-Revolution
    1. U-Substitution (Definite Integrals)
    2. Areas Between Curves (Intro)
    3. Area Between Curves
    4. Area Between 2 Curves
    5. Visualizing Volumes of Rotation
    6. Volume of Solid of Revolution about x-axis
    7. Disc Action!!!
    8. Solids of Revolution (Discs)
    9. Washer Action!!! (1)
    10. Washer Action !!! (2) - Calculus
    11. Cylindrical Shell Action!!! (1)
    12. Cylindrical Shell Action!!! (2)
    13. Parabola Around y-Axis
    14. Parabola Rotated Around y-Axis Wireframe
    15. Parabola Rotated Around x-Axis
    16. Parabola Rotated Around x-Axis
    17. Solids of Revolution: Around the x-Axis
    18. Solids of Revolution: Around the y-Axis
    19. Solids of Revolution: Around y=6
    20. Calculus Solids
    21. V. of Solid NOT of Revolution
    22. Cross-Sections Perpendicular to x-Axis: Squares
    23. Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
    24. Cross-Sections Perpendicular to x-Axis: Right Triangles
    25. Cross-Sections Perpendicular to x-Axis: Rectangles
    26. Areas & Volumes: Culminating Activity
  9. Average Value and Arc Length
    1. Average Value of a Function
    2. Arc Length (Calculus)
  10. Integration Techniques
    1. Apex Section 6.1-Integration using substitution
    2. Sine & Cosine of a Sum: Discovery
    3. Partial Fraction Decomposition Calculator
  11. Differential Equations
    1. Slope Field
    2. Copy of Slope Fields.
    3. Euler's Method
    4. Quiz: Writing Exponential Growth & Decay Functions
    5. Exponential Growth vs. Decay (Intro)
    6. Newton's Law of Cooling
    7. Logistic Growth Function
  12. Sequences & Series
    1. Sequences (Dynamic Illustrator)
    2. Convergent or Divergent Series
    3. Sum of Infinite Geometric Series
    4. Partial Sums Alternating Series
    5. Integral Test for Series
    6. Taylor Polynomials
  13. Parametric Equations
    1. Parametric Path on a Number Line
    2. Parametric Path
    3. Parametric Equations (I)
    4. Parametric Equations Grapher
    5. Parametric Equations: dy/dx (Ex 1)
    6. Cycloid Animation!
  14. Polar Coordinates
    1. Trig Function Values (30 Degrees)
    2. Trig Function Values (45 Degrees)
    3. Trig Function Values (60 Degrees)
    4. Special Angles in Standard Position: Intro (V1)
    5. Special Angles in Standard Position: Intro (V2)
    6. Special Angles in Standard Position: Intro (V3)
    7. Polar Coordinates: Introduction
    8. Writing Equivalent Polar Coordinates: Quiz
    9. Polar Function Grapher
    10. Derivatives in Polar Coordintes
    11. Areas with Polar Coordinates
    12. Area Between 2 Polar Graphs
    13. Arc Length in Polar Coordintes

1.

Preliminary Review Topics

  • 1. Pythagorean Trigonometric Identity (1)
  • 2. Trig ID Movie (II)
  • 3. Trig ID Movie (III)
  • 4. Exponential Functions: Graphs
  • 5. Logarithmic Functions: Graphs
  • 6. Logarithmic Action!
  • 7. Logarithmic Action (2)!
  • 8. Logarithmic Action (3)!
  • 9. Logarithmic Action (4)!

1.1.

–

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

2.

Limits & Continuity

  • 1. Limits: Introductory Questions
  • 2. One CRAZY Limit !!!
  • 3. CRAZY FUNCTION!!!
  • 4. A tool to explore delta-epsilon understandings.
  • 5. Cont in uity
  • 6. IVT Dynamic Illustrator
  • 7. Continuity Questions
  • 8. Vertical Asymptote (Defined as a Limit)
  • 9. Horizontal Asymptote (Defined as a Limit)
  • 10. One Special Limit

2.1.

–

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

2.10.

–

3.

Derivatives: Introduction & Intuition

  • 1. Average Velocity
  • 2. Average to Instantaneous (Intro)
  • 3. Sketch the Derivative (Warm Up)
  • 4. Drawing Derivatives
  • 5. Constructing Graphs of Derivative Functions (Intuitively)
  • 6. Average Rate of Change Intervals
  • 7. Average Rate of Change of a Function: Dynamic Illustration
  • 8. Average Rate of Change vs. Instantaneous Rate of Change
  • 9. Derivatives (Intro)-1
  • 10. Derivatives (Intro)-2
  • 11. Graphing The Derivative of a Function
  • 12. 3-Way Color-Changing Derivative Grapher
  • 13. When does f'(x) = f(x)?
  • 14. Mean Value Theorem
  • 15. Mean Value Theorem (Without Words)

3.1.

–

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

3.10.

–

3.11.

–

3.12.

–

3.13.

–

3.14.

–

3.15.

–

4.

Derivatives of Special Functions & Differentiation Techniques

  • 1. Derivative of a Product
  • 2. Important Trig Limits
  • 3. Derivative of Sine & Cosine Functions (Quick Investigation)
  • 4. Derivative of Tangent Function (Investigation)
  • 5. Implicit Differentiation: Intro
  • 6. Folium of Descartes
  • 7. Implicit Differentiation (Quick Check)
  • 8. Derivative of Arcsine Function
  • 9. Derivative of Arccosine Function
  • 10. Derivative of Arctangent Function
  • 11. Derivatives of Inverse Functions
  • 12. Derivative of Natural Log Function

4.1.

–

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

4.8.

–

4.9.

–

4.10.

–

4.11.

–

4.12.

–

5.

Related Rates & Linearization of Functions

  • 1. Related Rates (1)
  • 2. Related Rates (2)
  • 3. Falling Ladder !!!
  • 4. Related Rates (3)
  • 5. Related Rates: Adjustable Cone with dh/dt Constant
  • 6. Related Rates (Rolling Carts Problem)
  • 7. Linearization Illustrator (Calculus)
  • 8. Linearization Checker (Calculus)
  • 9. Newton's Method: Illustrated

5.1.

–

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

5.7.

–

5.8.

–

5.9.

–

6.

Closed Interval Method & Optimization Problems

  • 1. Critical Numbers & Critical Points of Functions (Intro)
  • 2. The Closed Interval Method (Application Problem)
  • 3. Optimization: Area of a Rectangle
  • 4. Minimizing the Area of a Triangle
  • 5. Optimization - Box
  • 6. Maximizing Trapezoid Area
  • 7. Optimization Challenge 1
  • 8. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
  • 9. Honeybee Population (Growth Rate Question)
  • 10. Oil Pipeline Optimization Problem
  • 11. Cylinder Inscribed Inside Sphere
  • 12. Cylinder Inscribed In Cone
  • 13. Distance From Point to Graph
  • 14. Optimization Problem: Isosceles Triangle Circumscribed about a Circle

6.1.

–

6.2.

–

6.3.

–

6.4.

–

6.5.

–

6.6.

–

6.7.

–

6.8.

–

6.9.

–

6.10.

–

6.11.

–

6.12.

–

6.13.

–

6.14.

–

7.

Riemann Sums; Indefinite and Definite Integrals

  • 1. Definite Integral Illustrator (I)
  • 2. Trapezoid: Area (I)
  • 3. Definite Integral Illustrator (II)
  • 4. Definite Integrals: Sum
  • 5. What Makes a Function Even?
  • 6. What Makes a Function Odd?
  • 7. Odd Functions: Another Look (Take 2)!
  • 8. Accumulations
  • 9. All Sums (Riemann Sums)

7.1.

–

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

–

7.8.

–

7.9.

–

8.

Areas and Volumes; Solids of Revolution & Non-Revolution

  • 1. U-Substitution (Definite Integrals)
  • 2. Areas Between Curves (Intro)
  • 3. Area Between Curves
  • 4. Area Between 2 Curves
  • 5. Visualizing Volumes of Rotation
  • 6. Volume of Solid of Revolution about x-axis
  • 7. Disc Action!!!
  • 8. Solids of Revolution (Discs)
  • 9. Washer Action!!! (1)
  • 10. Washer Action !!! (2) - Calculus
  • 11. Cylindrical Shell Action!!! (1)
  • 12. Cylindrical Shell Action!!! (2)
  • 13. Parabola Around y-Axis
  • 14. Parabola Rotated Around y-Axis Wireframe
  • 15. Parabola Rotated Around x-Axis
  • 16. Parabola Rotated Around x-Axis
  • 17. Solids of Revolution: Around the x-Axis
  • 18. Solids of Revolution: Around the y-Axis
  • 19. Solids of Revolution: Around y=6
  • 20. Calculus Solids
  • 21. V. of Solid NOT of Revolution
  • 22. Cross-Sections Perpendicular to x-Axis: Squares
  • 23. Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
  • 24. Cross-Sections Perpendicular to x-Axis: Right Triangles
  • 25. Cross-Sections Perpendicular to x-Axis: Rectangles
  • 26. Areas & Volumes: Culminating Activity

8.1.

–

8.2.

–

8.3.

–

8.4.

–

8.5.

–

8.6.

–

8.7.

–

8.8.

–

8.9.

–

8.10.

–

8.11.

–

8.12.

–

8.13.

–

8.14.

–

8.15.

–

8.16.

–

8.17.

–

8.18.

–

8.19.

–

8.20.

–

8.21.

–

8.22.

–

8.23.

–

8.24.

–

8.25.

–

8.26.

–

9.

Average Value and Arc Length

  • 1. Average Value of a Function
  • 2. Arc Length (Calculus)

9.1.

–

9.2.

–

10.

Integration Techniques

  • 1. Apex Section 6.1-Integration using substitution
  • 2. Sine & Cosine of a Sum: Discovery
  • 3. Partial Fraction Decomposition Calculator

10.1.

–

10.2.

–

10.3.

–

11.

Differential Equations

  • 1. Slope Field
  • 2. Copy of Slope Fields.
  • 3. Euler's Method
  • 4. Quiz: Writing Exponential Growth & Decay Functions
  • 5. Exponential Growth vs. Decay (Intro)
  • 6. Newton's Law of Cooling
  • 7. Logistic Growth Function

11.1.

–

11.2.

–

11.3.

–

11.4.

–

11.5.

–

11.6.

–

11.7.

–

12.

Sequences & Series

  • 1. Sequences (Dynamic Illustrator)
  • 2. Convergent or Divergent Series
  • 3. Sum of Infinite Geometric Series
  • 4. Partial Sums Alternating Series
  • 5. Integral Test for Series
  • 6. Taylor Polynomials

12.1.

–

12.2.

–

12.3.

–

12.4.

–

12.5.

–

12.6.

–

13.

Parametric Equations

Contains Parametric Equations Applets (Precalculus & Calculus)

  • 1. Parametric Path on a Number Line
  • 2. Parametric Path
  • 3. Parametric Equations (I)
  • 4. Parametric Equations Grapher
  • 5. Parametric Equations: dy/dx (Ex 1)
  • 6. Cycloid Animation!

13.1.

–

13.2.

–

13.3.

–

13.4.

–

13.5.

–

13.6.

–

14.

Polar Coordinates

  • 1. Trig Function Values (30 Degrees)
  • 2. Trig Function Values (45 Degrees)
  • 3. Trig Function Values (60 Degrees)
  • 4. Special Angles in Standard Position: Intro (V1)
  • 5. Special Angles in Standard Position: Intro (V2)
  • 6. Special Angles in Standard Position: Intro (V3)
  • 7. Polar Coordinates: Introduction
  • 8. Writing Equivalent Polar Coordinates: Quiz
  • 9. Polar Function Grapher
  • 10. Derivatives in Polar Coordintes
  • 11. Areas with Polar Coordinates
  • 12. Area Between 2 Polar Graphs
  • 13. Arc Length in Polar Coordintes

14.1.

–

14.2.

–

14.3.

–

14.4.

–

14.5.

–

14.6.

–

14.7.

–

14.8.

–

14.9.

–

14.10.

–

14.11.

–

14.12.

–

14.13.

–

Information