Calculus I materials

Kevin Hopkins

Materials that were originally at [url]https://sites.google.com/site/collegealgebraworksheets/calculus-i-illustrations[/url] and [url]https://sites.google.com/site/collegealgebraworksheets/calculus-i-worksheets[/url] that are being moved to geogebratube. Hopefully students can use them easier here. Some are "self check" and others have you enter the answer and GeoGebra does the checking. I would encourage you to watch an introductory video ([url]http://youtu.be/zzz42Y_qZJw[/url]) to get a feel for how the worksheets operate. The book these worksheets were written for is the 7th edition of Stewart's Calculus book. That should explain the section numbers you will see. Other textbooks should have this material in them, but probably not with the same sections. There are also some for Precalculus review (with some overlap as there is some review in the Appendix of the Stewart book): [url]http://www.geogebratube.org/student/b85255[/url]. One might also be interested in the Briggs/Cochran/Schulz Calculus ebook with interactive figures, [url]http://www.pearsonhighered.com/briggscochran1einfo/detail/technology/index.html [/url] or Mathematica Demonstrations in a similar vein that are at [url]http://demonstrations.wolfram.com/ [/url]. Feel free to email me at khopkins@sbuniv.edu if you think there is an error in any worksheet (please be as specific as possible-a screenshot of the error would be most helpful). I tested them quite a bit, but there could be things that come up that I didn’t encounter in my testing. I would also like to know if you used these and found them useful. If so, can you think of ways I could expand them?

Table of Contents

  1. Illustrations for Class-Appendix and Chapter 1
    1. Appendix A-Really an overview of ideas for the entire course
    2. Appendix B-Lines
    3. Appendix C-Equations of Circles
    4. Representing a Function in Four Ways-Section 1.1
    5. Graphing Functions-Section 1.1
    6. Function Table-Section 1.3
    7. Function Graphs-Section 1.3
    8. Function Rule-Section 1.3
    9. Section 1.1-Piecewise Defined Functions
    10. Section 1.3-Transformations of functions-Translations
    11. Section 1.3-Transformations of functions-Reflections
    12. Section 1.3-Transformations of functions-Stretches
    13. Section 1.3-Graph of f(x) vs 1/f(x) and abs(f(x))
    14. Section 1.4-Tangent Lines with Input
    15. Section 1.4-Tangent Lines as Limits of Secant Lines/Sliders
    16. Section 1.4-Tangent Lines as Limits of Secant Lines/Input
    17. Section 1.7-Formal Definition of the Limit
    18. Section 1.8-Intermediate Value Theorem
    19. Section 1.8-Bisection Method-Related to Intermediate Val Thm
    20. Section 1.8-Secant Method-Related to Intermediate Value Thm
    21. Perpendicular and Parallel Lines-Section 2.7-2.8
  2. Illustrations for Class-Chapter 2
    1. Section 2.2-Differentiability
    2. Appendix D (covered after section 2.3)-Graph of Sin(x)
    3. Appendix D (covered after section 2.3)-Graph of Cos(x).
    4. Appendix D (covered after section 2.3)-Graph of Tan(x)
    5. Section 2.6-Implicit Differentiation
    6. Section 2.7-Particle Motion
    7. Section 2.8-Related Rates-Ladder Falling
    8. Section 2.8-Related Rates-Man Walking
    9. Section 2.8-Related Rates-Rotating Spotlight
    10. Section 2.8-Related Rates-Boat Pulling
    11. Section 2.9-Differential
  3. Illustrations for Class-Chapters 3-5
    1. Section 3.2-Mean Value Theorem
    2. Section 3.4-Asymptotes
    3. Section 3.5-Curve Sketching
    4. Section 3.7-Applied Max Min
    5. Section 3.8-Newton's Method
    6. Section 4.1-Riemann Sums-Equal Subintervals
    7. Section 4.1-Riemann Sums-Random Width Intervals
    8. Section 4.3: Fundamental Theorem of Calculus, Part I
    9. Section 4.3-Fundamental Theorem of Calculus
    10. Section 5.1-Areas
    11. Section 5.2-Method of Disks
    12. Method of Washers-Section 5.2
    13. Method of Shells-Section 5.3
  4. Worksheets for student practice-Appendix and Ch 1
    1. Appendix A-Absolute Value equations
    2. Solving Linear Inequalities
    3. Appendix A-Solving Absolute Value Inequalities
    4. Appendix A-Solving Quadratic Inequalities
    5. Appendix A-Solving Polynomial Inequalities
    6. Appendix A-Solving Rational Inequalities
    7. Appendix B-Slope Intercept Form
    8. Appendix C-Equations of Circles
    9. Section 1.1-Increasing and Decreasing Functions
    10. Section 1.1-Concavity
    11. Work with difference quotient
    12. Section 1.3-Function Transformation-Easiest
    13. Section 1.3-Function Transformation-More Difficult
    14. Section 1.3-Combining Functions
    15. Section 1.3-Function Composition-reversing.
    16. Section 1.5-Estimating Limits from Given Functions
    17. Section 1.5-Estimating Limits-User enter the Function
    18. Section 1.5-Limits of Piecewise Functions
    19. Section 1.6-Limits
  5. Worksheets for student practice-Chapters 2-5
    1. Section 2.2-Sketching Graph of Derivative
    2. Section 2.2-Sketching Graph of Derivative
    3. Section 2.2 Derivative Matching
    4. Section 2.3 and 2.5
    5. Trig values for standard angles
    6. Find Angle from Trig Function Value
    7. Section 2.5-Chain Rule
    8. Section 2.6-Implicit Differentiation
    9. Section 3.3-Graphing f from sign of f'(x).
    10. Section 4.3-Area via Integrals as Opposed to Rectangles
    11. Section 4.4-Indefinite Integrals
    12. Section 4.5-Integration using substitution

1.

Illustrations for Class-Appendix and Chapter 1

  • 1. Appendix A-Really an overview of ideas for the entire course
  • 2. Appendix B-Lines
  • 3. Appendix C-Equations of Circles
  • 4. Representing a Function in Four Ways-Section 1.1
  • 5. Graphing Functions-Section 1.1
  • 6. Function Table-Section 1.3
  • 7. Function Graphs-Section 1.3
  • 8. Function Rule-Section 1.3
  • 9. Section 1.1-Piecewise Defined Functions
  • 10. Section 1.3-Transformations of functions-Translations
  • 11. Section 1.3-Transformations of functions-Reflections
  • 12. Section 1.3-Transformations of functions-Stretches
  • 13. Section 1.3-Graph of f(x) vs 1/f(x) and abs(f(x))
  • 14. Section 1.4-Tangent Lines with Input
  • 15. Section 1.4-Tangent Lines as Limits of Secant Lines/Sliders
  • 16. Section 1.4-Tangent Lines as Limits of Secant Lines/Input
  • 17. Section 1.7-Formal Definition of the Limit
  • 18. Section 1.8-Intermediate Value Theorem
  • 19. Section 1.8-Bisection Method-Related to Intermediate Val Thm
  • 20. Section 1.8-Secant Method-Related to Intermediate Value Thm
  • 21. Perpendicular and Parallel Lines-Section 2.7-2.8

1.1.

Appendix A-Really an overview of ideas for the entire course

Ideas related to solving a problem.
– Kevin Hopkins

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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1.17.

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1.18.

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1.19.

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1.20.

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1.21.

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2.

Illustrations for Class-Chapter 2

  • 1. Section 2.2-Differentiability
  • 2. Appendix D (covered after section 2.3)-Graph of Sin(x)
  • 3. Appendix D (covered after section 2.3)-Graph of Cos(x).
  • 4. Appendix D (covered after section 2.3)-Graph of Tan(x)
  • 5. Section 2.6-Implicit Differentiation
  • 6. Section 2.7-Particle Motion
  • 7. Section 2.8-Related Rates-Ladder Falling
  • 8. Section 2.8-Related Rates-Man Walking
  • 9. Section 2.8-Related Rates-Rotating Spotlight
  • 10. Section 2.8-Related Rates-Boat Pulling
  • 11. Section 2.9-Differential

2.1.

Section 2.2-Differentiability

A look at what would make a derivative not exist.
– Kevin Hopkins

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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3.

Illustrations for Class-Chapters 3-5

  • 1. Section 3.2-Mean Value Theorem
  • 2. Section 3.4-Asymptotes
  • 3. Section 3.5-Curve Sketching
  • 4. Section 3.7-Applied Max Min
  • 5. Section 3.8-Newton's Method
  • 6. Section 4.1-Riemann Sums-Equal Subintervals
  • 7. Section 4.1-Riemann Sums-Random Width Intervals
  • 8. Section 4.3: Fundamental Theorem of Calculus, Part I
  • 9. Section 4.3-Fundamental Theorem of Calculus
  • 10. Section 5.1-Areas
  • 11. Section 5.2-Method of Disks
  • 12. Method of Washers-Section 5.2
  • 13. Method of Shells-Section 5.3

3.1.

Section 3.2-Mean Value Theorem

Illustrate the mean value theorem, a consequence of differentiability.
Section 3.2-Mean Value Theorem
– Kevin Hopkins

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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4.

Worksheets for student practice-Appendix and Ch 1

  • 1. Appendix A-Absolute Value equations
  • 2. Solving Linear Inequalities
  • 3. Appendix A-Solving Absolute Value Inequalities
  • 4. Appendix A-Solving Quadratic Inequalities
  • 5. Appendix A-Solving Polynomial Inequalities
  • 6. Appendix A-Solving Rational Inequalities
  • 7. Appendix B-Slope Intercept Form
  • 8. Appendix C-Equations of Circles
  • 9. Section 1.1-Increasing and Decreasing Functions
  • 10. Section 1.1-Concavity
  • 11. Work with difference quotient
  • 12. Section 1.3-Function Transformation-Easiest
  • 13. Section 1.3-Function Transformation-More Difficult
  • 14. Section 1.3-Combining Functions
  • 15. Section 1.3-Function Composition-reversing.
  • 16. Section 1.5-Estimating Limits from Given Functions
  • 17. Section 1.5-Estimating Limits-User enter the Function
  • 18. Section 1.5-Limits of Piecewise Functions
  • 19. Section 1.6-Limits

4.1.

Appendix A-Absolute Value equations

Practice solving absolute value equations.
– Kevin Hopkins

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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4.14.

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4.15.

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4.16.

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4.17.

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4.18.

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4.19.

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5.

Worksheets for student practice-Chapters 2-5

  • 1. Section 2.2-Sketching Graph of Derivative
  • 2. Section 2.2-Sketching Graph of Derivative
  • 3. Section 2.2 Derivative Matching
  • 4. Section 2.3 and 2.5
  • 5. Trig values for standard angles
  • 6. Find Angle from Trig Function Value
  • 7. Section 2.5-Chain Rule
  • 8. Section 2.6-Implicit Differentiation
  • 9. Section 3.3-Graphing f from sign of f'(x).
  • 10. Section 4.3-Area via Integrals as Opposed to Rectangles
  • 11. Section 4.4-Indefinite Integrals
  • 12. Section 4.5-Integration using substitution

5.1.

Section 2.2-Sketching Graph of Derivative

Sketching graph of derivative given the graph of a function, which you can enter your own function here.
– Kevin Hopkins

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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