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Introducing Limits with Graphs and Tables

Introducing Limits with Graphs and Tables
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2020-08-01 00:07
FunctionLimitGraphing
This example introduces the concept of limits through graphs and tables. It first demonstrates the intuitive meaning of limits through function graphs, and then verifies the calculation results using table data. Commands used include Textfield, Vector, OrthogonalLine, Intersect, and Point. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. Textfield(c) → InputBox2
  3. Textfield(delta) → InputBox3
  4. Vector(C, E) → u
  5. Vector(B, D) → v
  6. OrthogonalLine(E, xAxis) → g
  7. OrthogonalLine(D, xAxis) → h
  8. Intersect(f, g, (-2.455, 3.197802197802197)) → L
  9. Intersect(f, h, (-0.945, 0.052132701421800993)) → R
  10. OrthogonalLine(L, yAxis) → i
  11. OrthogonalLine(R, yAxis) → j
  12. Intersect(j, yAxis) → G
  13. Intersect(i, yAxis) → H
  14. Vector(E, L) → w
  15. Vector(L, H) → a
  16. Vector(D, R) → b
  17. Vector(R, G) → d
  18. OrthogonalLine(C, xAxis) → k
  19. OrthogonalLine(B, xAxis) → l
  20. Intersect(f, k, (-2.7, 2.4285714285714284)) → A_1
  21. Intersect(f, l, (-0.7, 0.2307692307692308)) → F
  22. OrthogonalLine(A_1, yAxis) → m
  23. OrthogonalLine(F, yAxis) → n
  24. Intersect(n, yAxis) → I
  25. Intersect(m, yAxis) → J
  26. Vector(J, H) → e
  27. Vector(I, G) → p
  28. Point(f) → A

AI Drawing Prompt Reference

Draw a function graph by entering the function expression f(x) in the input box, and mark points A and A_1 on the graph. Draw a vertical line m from point A to the y-axis, and draw a vertical line n from point A_1 to the y-axis. The intersection of line n with the y-axis is point I, and the intersection of line m with the y-axis is point J. Then, draw points C and B, and draw a vertical line k from point C to the x-axis, and draw a vertical line l from point B to the x-axis. The intersection of line l with the function graph is point F, and the intersection of line k with the function graph is point A_1. Next, draw points E and D, and draw a vertical line g from point E to the x-axis, and draw a vertical line h from point D to the x-axis. The intersection of line h with the y-axis is point G, and the intersection of line g with the y-axis is point H. Finally, draw points L and R, and draw a vertical line i from point L to the y-axis, and draw a vertical line j from point R to the y-axis. The intersection of line j with the y-axis is point G, and the intersection of line i with the y-axis is point H.
The prompt above was compiled from the original drawing commands and is for reference only.