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Example of One-Sided Limits for a Square Root Function

Example of One-Sided Limits for a Square Root Function
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2016-09-20 16:53
FunctionCalculusLimit
This example demonstrates the one-sided limits of a square root function. It involves the concept of limits and is presented using both tabular and graphical methods. The construction uses GeoGebra objects such as functions and slider animations. Suitable for high school mathematics education and learning about limits.

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 the graph of the square root function f(x) = 3x divided by (sqrt(x+1) - 1). Show points on the graph for x-values approaching 0 from both sides, such as -0.01, -0.001, -0.0001, and their positive counterparts, with corresponding y-values. Mark the limit at x=0 with an open circle. Include a table listing these x-values and f(x) values to illustrate one-sided limits. The graph should clearly show the behavior near x=0, with labels for left and right limits.
The prompt above was compiled from the original drawing commands and is for reference only.