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Taylor Series Expansion Demo

Taylor Series Expansion Demo
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2018-11-07 19:54
FunctionTrigonometryGeometric Construction
This example demonstrates the Taylor series expansion of a function f(x) around x=0. It involves core mathematical concepts such as function approximation, infinite series, and properties of trigonometric functions. Key GeoGebra commands used include Point, Segment, Polygon, Text, Sequence, and Midpoint to construct function graphs, polynomial approximations, and dynamic visualizations. Suitable for high school students and math enthusiasts to understand function approximation theory and the geometric meaning of Taylor series.

GeoGebra Commands & Parameters

  1. Point(Circle[A, abs((a * q))]) → B
  2. Segment(A, B) → c
  3. Polygon(A + (abs(c), 0), A + (abs(c), 6), A + (0, 6), A) → poly1, d, e, f, n
  4. Polygon(C + (abs(r), 0), C + (abs(r), 6), C + (0, 6), C) → poly2, g, h, i, p
  5. Polygon(D + (abs(b), 0), D + (abs(b), 6), D + (0, 6), D) → poly3, j, k, l, m
  6. Text(("a=" * a)) → text3
  7. Text(("b=" * b)) → text4
  8. Text(("q=" * q)) → text5
  9. Text(("r=" * r)) → text6
  10. Text("b", D + (abs(b) / 2, 2.4)) → text1
  11. Sequence(Text["a", A + (abs(a) / 2 + (abs(a) * p), 2.4)], p, 0, q - 1) → list2
  12. Sequence(Segment[A + ((i * abs(a)), 0), A + ((i * abs(a)), 6)], i, 1, q) → list1
  13. Text("r", A + ((q * abs(a)) + abs(r) / 2, 2.4)) → text2
  14. Midpoint(Midpoint[Corner[4], Midpoint[Corner[4], Midpoint[Corner[4], Corner[1]]]], Midpoint[Corner[4], Midpoint[Corner[4], Corner[1]]]) → O
  15. Midpoint(Midpoint[Corner[3], Midpoint[Corner[3], Midpoint[Corner[3], Corner[2]]]], Midpoint[Corner[3], Midpoint[Corner[3], Corner[2]]]) → P