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Calculus of Limits

Calculus of Limits
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2018-01-24 03:29
FunctionSequenceCalculusLimitGraphing
This example demonstrates the concept of limits and their calculations. Key mathematical concepts include limits, functions, and sequences. Using GeoGebra commands such as Point, Element, Vector, and Sequence, the process of limit calculation is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Element(ops, bin_{op}) → op
  3. Element(fnlist, comb_{op}) → o
  4. Vector(A, B) → u
  5. Vector(A, C) → v
  6. Vector(B, D) → w
  7. Vector(C, D) → a
  8. Vector(A, B) → b
  9. Vector(B, E) → c
  10. Vector(A, F) → d
  11. Vector(F, E) → e
  12. Vector(B, E) → h
  13. Sequence(-5, 5) → list1
  14. Zip((a1, b), b, list1) → list2
  15. Zip((a2, b), b, list1) → list3
  16. Zip((a3, b), b, list1) → list4
  17. Textfield(f) → InputBox1
  18. Textfield(g) → InputBox2
  19. Sequence(y(A) - δ, y(A) + δ, δ / 5) → L_1
  20. Zip((0, t), t, L_1) → delint
  21. Zip((a1, f(t)), t, L_1) → delintf
  22. Zip((a2, g(t)), t, L_1) → delintg
  23. Zip((a3, o(t)), t, L_1) → delinto
  24. Zip(Vector[A, B], A, delint, B, delintf) → vecf
  25. Zip(Vector[A, B], A, delint, B, delintg) → vecg
  26. Zip(Vector[A, B], A, delintf, B, delinto) → vecfo
  27. Zip(Vector[A, B], A, delintg, B, delinto) → vecgo
  28. Sequence(f(y(A)) - δ', f(y(A)) + δ', δ' / 5) → L_2
  29. Zip((a2, g(t)), t, L_2) → del'intg
  30. Zip((a1, t), t, L_2) → del'int
  31. Zip(Vector[A, B], A, del'int, B, del'intg) → vecg'
  32. TableText({{A1, B1, C1, D1}, {A2, B2, C2, D2}, {A3, B3, C3, D3}, {A4, B4, C4, D4}, {A5, B5, C5, D5}, {A6, B6, C6, D6}, {A7, B7, C7, D7}, {A8, B8, C8, D8}, {A9, B9, C9, D9}, {A10, B10, C10, D10}, {A11, B11, C11, D11}, {A12, B12, C12, D12}}, "|_cccc") → text14

AI Drawing Prompt Reference

Draw a graph of a function's limit, including the function's graph and points A, B, C, D, E, F, as well as vectors from point A to these points. Use point A as the starting point to draw vectors from A to B, C, D, E, and F, and show the dynamic changes of these vectors to intuitively demonstrate the concept of limits.
The prompt above was compiled from the original drawing commands and is for reference only.