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Continuity and Differentiability Demo

Continuity and Differentiability Demo
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2016-03-18 18:38
FunctionCalculusGeometric Construction
This example demonstrates the concepts of continuity and differentiability through dynamic geometry. It involves core math concepts like continuity, differentiability, function graphs, line segments, and limits. GeoGebra commands used include Line, Circle, Intersect, Segment, Point, and OrthogonalLine. Suitable for high school and above learners to understand basic calculus concepts.

GeoGebra Commands & Parameters

  1. Line(A, B) → b
  2. Circle(C, D) → c
  3. Intersect(c, b) → E, F
  4. Segment(E, F) → d
  5. Point(g) → G
  6. Point(g) → H
  7. Segment(H, G) → e
  8. Point(h) → I
  9. Point(h) → J
  10. Segment(I, J) → i
  11. Line(K, L) → q
  12. Circle(M, N) → r
  13. Intersect(r, q, 2) → O
  14. Intersect(r, q, 1) → P
  15. Segment(O, P) → s
  16. OrthogonalLine(K, xAxis) → t
  17. Intersect(r, t) → Q, R
  18. Segment(R, Q) → a_1
  19. Line(A, S) → c_1
  20. Circle(T, U) → d_1
  21. Intersect(d_1, c_1) → V, W
  22. Segment(W, V) → e_1
  23. Line(B_1, A) → l_1
  24. Circle(Z, C_1) → q_1
  25. Intersect(q_1, l_1) → D_1, E_1
  26. Segment(E_1, D_1) → n_1
  27. Line(F_1, H_1) → t_1
  28. Circle(I_1, J_1) → c_2
  29. Intersect(c_2, t_1) → K_1, L_1
  30. Segment(K_1, L_1) → a_2