Calculus Applets using GeoGebra

This website is a project by Marc Renault, supported by Shippensburg University. My goal is to make a complete library of applets for Calculus I that are suitable for in-class demonstrations and/or student exploration. I have created these applets using GeoGebra, wonderful (free!) software for creating dynamic visualizations of mathematical ideas.


  1. Intuitive Notion of the Limit
  2. Intuitive Notion of the Limit - One-Sided Limits
  3. The Limit Laws
  4. Continuity at a Point
  5. An Important Trig Limit `lim_(theta-->0) (sin(theta))/theta = 1`
  6. Average and Instantaneous Rate of Change
  7. Differentiation

  8. The Derivative at a Point
  9. The Derivative as a Function
  10. The Derivative of Elementary Functions
  11. Try to Graph the Derivative Function
  12. The Derivative of Exponential Functions
  13. Identify the Derivative Function
  14. Derivatives and Graph Transformations
  15. Identify a Function and its First and Second Derivatives
  16. Identify an Antiderivative Function
  17. The Power Rule - Derivatives of Polynomial Functions
  18. Intuitive Notion of the Chain Rule
  19. Implicit Differentiation
  20. Derivatives of Inverse Functions
  21. Applications of the Derivative

  22. First derivative test - Reconstruct `f` from its First Derivative
  23. Second derivative test - Reconstruct `f` from its Second Derivative
  24. Derivatives and the Shape of a Graph
  25. Related Rates Problems: Oil Slick -- A Falling Ladder -- A Conical Tank -- Driving Car -- Lamppost -- Two Trains -- Searchlight -- Rocket Launch
  26. Optimization Problems: Bending a Wire -- Rectangle Inscribed in a Parabola -- Three Pens -- Getting Power to an Island -- Another Wire Problem -- Function and Rectangle 1 -- Function and Rectangle 2 -- Triangle Circumscribing a Circle --
  27. The Integral

  28. Introduction to Integration - The Exercise Bicycle Problem:   Part 1     Part 2
  29. Introduction to Integration - Gaining Geometric Intuition
  30. The Riemann Sum
  31. The Area Function
  32. The Fundamental Theorem of Calculus, Part I (Theoretical Part)
  33. The Fundamental Theorem of Calculus, Part II (Practical Part)

Additional Resources

Creative Commons License
Calculus Applets using GeoGebra by Marc Renault is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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