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极限唯一性定理与证明

极限唯一性定理与证明
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2018-01-21 07:37
微积分导数极限几何作图
①本范例演示极限唯一性的数学定理与证明过程；②涉及的核心数学概念为极限的唯一性定理，是微积分中的基础内容；③作图要点——从下方『构造摘要』提炼用到了Point, Vector, Textfield, Segment, Line, Derivative, Intersect, Polygon, Sequence等GeoGebra命令/对象；④适合大学或高中高年级学生学习微积分，用于直观理解极限定理。

GeoGebra 命令及参数

  1. Point(Target) → M1
  2. Point(Target) → LIM
  3. Point(yAxis) → A
  4. Vector(A, LIM) → f_2
  5. Textfield(f) → inputBox1
  6. Vector(x_1, y_1) → v
  7. Segment(f_a, F) → c
  8. Segment(E, F) → d
  9. Segment(A, x_1) → e
  10. Segment(LIM, y_1) → g
  11. Segment(LIM, y_1) → h
  12. Line(x_1, y_1) → i
  13. Derivative(f) → q
  14. Segment(C, D) → b
  15. Segment((0, y(A) - δ), (0, y(A) + δ)) → m
  16. Point(yAxis) → I
  17. Vector(I, J) → u
  18. Intersect(n, p) → K
  19. Intersect(a, p) → L
  20. Intersect(a, r) → M
  21. Intersect(n, r) → N
  22. Polygon(K, L, M, N) → epsdelt_1, k_1, l_1, m_1, n_1
  23. Sequence((0, xk), xk, y(A) - δ, y(A) + δ, δ / 8) → testx
  24. Sequence((2, f(xk)), xk, y(A) - δ, y(A) + δ, δ / 8) → testy
  25. Sequence(Vector[(0, xk), (2, f(xk))], xk, y(A) - δ, y(A) + δ, δ / 8) → list1
  26. Textfield(ε) → inputBox3
  27. Textfield(δ) → inputBox4
  28. Segment(A, G) → l
  29. Sequence(Vector[(0, xk), (2, f(xk))], xk, y(A) + δ / 8, y(A) + δ, δ / 8) → list2
  30. Intersect(a, r) → B
  31. Intersect(a, p) → O
  32. Intersect(p, a_1) → P
  33. Intersect(r, a_1) → Q
  34. Polygon(B, O, P, Q) → epsdelt, b_1, o_1, p_1, q_1
  35. Segment(M10, M11) → f_1