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Limits of Function Compositions

Limits of Function Compositions
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2018-06-25 04:47
FunctionCalculusLimit
This example demonstrates the concept of limits of function compositions. It involves key mathematical concepts such as functions and limits. Using GeoGebra commands like If, objects f, g, h, etc., it dynamically shows the process of limits of function compositions. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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