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函数复合的极限

函数复合的极限
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2018-06-25 04:47
函数微积分极限
这个范例演示了函数复合的极限概念。它涉及的核心数学概念包括函数、极限和复合函数。通过使用GeoGebra命令如If、对象f、g、h等，可以动态展示函数复合的极限过程。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. If(slider ≤ 0.99, (slider - 2, (1.5 * (slider - 2)) + 0.5), (0.99 - 2, (1.5 * (0.99 - 2)) + 0.5)) → J
  2. If(slider > 0.99, (slider - 3, (3 * (slider - 3)) + 1), (-5, -5)) → I
  3. If(slider < 0.99, ((-slider), (-slider) + 1), (-0.99, -0.99 + 1)) → L
  4. If(slider > 0.99, ((-slider) + 2, (-((-slider) + 1)^(2)) + 1), (-5, -5)) → K
  5. If(slider < 0.99, (slider - 1, slider), (0.99 - 1, 0.99)) → N
  6. If(slider > 0.99, (slider - 1, (-(slider - 2)^(2)) + 1), (-5, -5)) → M
  7. If(slider < 0.99, ((-slider) + 1, (-slider) + 2), (-0.99 + 1, -0.99 + 2)) → P
  8. If(slider > 0.99, ((-slider) + 3, (-((-slider) + 2)^(2)) + 1), (-5, 5)) → O
  9. If(slider < 0.99, (slider, slider + 1), (0.99, 1.99)) → R
  10. If(slider > 0.99, (slider, (-(slider - 1)^(2)) + 1), (-5, -5)) → Q
  11. If(slider < 0.99, ((-slider) + 2, (-slider) + 3), (-0.99 + 2, -0.99 + 3)) → T
  12. If(slider > 0.99, ((-slider) + 4, (-((-slider) + 3)^(2)) + 1), (-5, -5)) → S
  13. If(slider < 0.99, (slider + 1, slider + 2), (1.99, 2.99)) → V
  14. If(slider > 0.99, (slider + 1, (-slider^(2)) + 1), (-5, -5)) → U
  15. If(slider < 0.99, ((-slider) + 3, (-3 * ((-slider) + 3)) + 10), (-0.99 + 3, (-3 * (-0.99 + 3)) + 10)) → Z
  16. If(slider > 0.99, (slider + 2, -3), (-5, -5)) → W
  17. If(slider < 0.99, (slider - 2, (3 * (slider - 2)) + 1), (0.99 - 2, (3 * (0.99 - 2)) + 1)) → A_1
  18. If(slider > 0.99, (slider - 4, (1.5 * (slider - 4)) + 0.5), (-5, -5)) → B_1
  19. If(slider < 0.99, ((-slider), (-((-slider) - 1)^(2)) + 1), (-0.99, (-(-0.99 - 1)^(2)) + 1)) → C_1
  20. If(slider > 0.99, ((-slider) - 1, (1.5 * ((-slider) - 1)) + 0.5), (-5, -5)) → D_1
  21. If(slider > 0.99, (slider - 2, slider - 1), (-5, -5)) → F_1
  22. If(slider < 0.99, (slider - 1, (-(slider - 2)^(2)) + 1), (0.99 - 1, (-(0.99 - 2)^(2)) + 1)) → E_1
  23. If(slider < 0.99, ((-slider) + 1, (-((-slider))^(2)) + 1), (-0.99 + 1, (-(-0.99)^(2)) + 1)) → G_1
  24. If(slider > 0.99, ((-slider) + 2, (-slider) + 3), (-5, -5)) → H_1
  25. If(slider < 0.99, (slider, (-(slider - 1)^(2)) + 1), (0.99, (-(0.99 - 1)^(2)) + 1)) → I_1
  26. If(slider > 0.99, (slider - 1, slider), (-5, -5)) → J_1
  27. If(slider < 0.99, ((-slider) + 2, (-((-slider) + 1)^(2)) + 1), (-0.99 + 2, (-(-0.99 + 1)^(2)) + 1)) → K_1
  28. If(slider > 0.99, (slider - 1, slider), (-5, 5)) → L_1
  29. If(slider < 0.99, (slider + 1, (-slider^(2)) + 1), (0.99 + 1, (-0.99^(2)) + 1)) → M_1
  30. If(slider > 0.99, ((-slider) + 2, (-slider) + 3), (-5, -5)) → N_1
  31. If(slider < 0.99, ((-slider) + 3, (-((-slider) + 2)^(2)) + 1), (-0.99 + 3, (-(-0.99 + 2)^(2)) + 1)) → O_1
  32. If(slider > 0.99, (slider - 2, slider - 1), (-5, -5)) → P_1
  33. If(slider < 0.99, (slider + 2, (-3 * (slider + 2)) + 10), (0.99 + 2, (-3 * (0.99 + 2)) + 10)) → Q_1
  34. If(slider > 0.99, ((-slider) + 3, (-((-slider) + 2)^(2)) + 1), (-5, -5)) → R_1
  35. If(slider < 0.99, ((-slider) + 4, (-3 * ((-slider) + 4)) + 10), (-0.99 + 4, (-3 * (-0.99 + 4)) + 10)) → S_1
  36. If(slider > 0.99, (slider - 1, (-(slider - 2)^(2)) + 1), (-5, -5)) → T_1
  37. If(slider < 0.99, (slider + 2, (-(slider + 1)^(2)) + 1), (2.99, (-1.99^(2)) + 1)) → U_1
  38. If(slider > 0.99, ((-slider) - 1, (1.5 * ((-slider) - 1)) + 0.5), (-5, -5)) → V_1
  39. If(slider < 0.99, ((-slider) + 4, -3), (-0.99 + 4, -3)) → W_1
  40. If(slider < 0.99, Segment[(-10, -10), (-9, -9)], Segment[(-3, -4), ((3 * slider) - 6, -4)]) → i
  41. If(slider < 0.99, Segment[(-10, -10), (-9, -9)], Segment[(-3, -4), (-3, (4 * slider) - 8)]) → j