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泰勒级数展开演示

泰勒级数展开演示
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2018-11-07 19:54
函数三角函数几何作图
①本范例演示了函数f(x)在x=0处的泰勒级数展开过程；②涉及核心数学概念包括函数逼近、无限级数、三角函数性质；③作图要点：使用Point, Segment, Polygon, Text, Sequence, Midpoint等命令构造函数图像、多项式逼近及动态演示；④适合高中及以上学生及数学爱好者用于理解函数逼近理论及泰勒级数的几何意义。

GeoGebra 命令及参数

  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