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Intro to Limits Example: Tabular and Graphical

Intro to Limits Example: Tabular and Graphical
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2015-03-12 05:06
FunctionLimitGraphing
This example demonstrates calculating two one-sided limits on a square root function using both tabular and graphical methods. It involves core math concepts like limits, one-sided limits, and function graphs. The construction uses GeoGebra commands/objects such as f (function), points A1-A10 and B1-B10, leftOut and rightOut, text1 and text2, distance d, parameter a, points A and B, and slider animations. Suitable for high school calculus students to understand limit concepts and function behavior.

GeoGebra Commands & Parameters

  1. f(x) = ((3 * x)) / (sqrt(x + 1) - 1)
  2. Numeric A2(-0.01)
  3. A2 / 10
  4. A3 / 10
  5. A4 / 10
  6. Numeric A6(0.0)
  7. (-A5)
  8. (A7 * 10)
  9. (A8 * 10)
  10. (A9 * 10)
  11. f(A2)
  12. f(A3)
  13. f(A4)
  14. f(A5)
  15. f(A6)
  16. f(A7)
  17. f(A8)
  18. f(A9)
  19. f(A10)
  20. Numeric d(0.1)
  21. Numeric a(0.0)
  22. (a - d, f(a - d))
  23. (a + d, f(a + d))
  24. y(A)
  25. y(B)
  26. f

AI Drawing Prompt Reference

Draw a square root function graph to demonstrate the left and right limits as x approaches -1. Use both tabular and graphical methods, and adjust parameters a and d to observe the function behavior. First, plot the function f(x) = (3x) / (sqrt(x + 1) - 1), then add points A and B representing the function values at x=a-d and x=a+d, respectively. Finally, use the slider to adjust the values of a and d and observe the limit changes near x=-1.
The prompt above was compiled from the original drawing commands and is for reference only.