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MacLaurin Polynomials and Mapping Diagrams

MacLaurin Polynomials and Mapping Diagrams
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2015-03-06 14:02
FunctionCalculusDerivativeGraphing
This example demonstrates MacLaurin polynomials and their corresponding mapping diagrams and graphs. It covers the concept of MacLaurin polynomials and how to use GeoGebra to draw the approximations of polynomial functions. By using commands like Point, TaylorSeries, Vector, Textfield, users can dynamically adjust the degree and center of the polynomial, observing the relationship between the polynomial and the original function. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → P_x
  2. TaylorSeries(f, 0, n) → P_n
  3. Vector(P_x, B) → u
  4. Textfield(f) → inputBox1
  5. Textfield(f) → inputBox2
  6. Textfield(a) → inputBox3
  7. Textfield(b) → inputBox4
  8. Sequence((0, k), k, a, b, Δx) → SourcePtsMD
  9. Segment((0, a), (0, b)) → c
  10. Vector(P_x, F_x) → v
  11. Vector(P_x, P_1) → w
  12. Sequence((k, R_n(k)), k, a, b, Δx) → Graphpts
  13. Sequence(Vector[(0, k), (2, (y_{zoom} * R_n(k)))], k, a, b, Δx) → MD
  14. Sequence((2, (y_{zoom} * R_n(k))), k, a, b, Δx) → TargPts_1
  15. Derivative(f, A3) → B3
  16. Derivative(f, A4) → B4
  17. Derivative(f, A5) → B5
  18. Derivative(f, A6) → B6
  19. Derivative(f, A7) → B7
  20. Derivative(f, A8) → B8
  21. Derivative(f, A9) → B9
  22. Derivative(f, A10) → B10
  23. Derivative(f, A11) → B11
  24. Derivative(f, A12) → B12
  25. Derivative(f, A13) → B13
  26. Derivative(f, A14) → B14
  27. Derivative(f, A15) → B15
  28. Derivative(f, A16) → B16
  29. Derivative(f, A17) → B17
  30. Derivative(f, A18) → B18