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无穷极限探索器

无穷极限探索器
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2018-09-15 02:49
函数解析几何微积分极限滑块动画
①本范例演示函数在无穷远处的极限行为及图像变化；②涉及核心数学概念包括极限、分数、相似三角形、坐标几何、连续性与中值定理；③作图要点运用了GeoGebra命令对象：f, g, n_0, n_1, n_2, n_3, d_0, d_1, d_2, d_3, n_lead, d_{lead}, p_{lead}, q_{lead}, r, h；④适合高中及以上数学学习者，用于理解极限理论及函数性质。

GeoGebra 命令及参数

  1. f(x) = ((5 * x^(2)) - (7 * x)) / (x^(3) + 12)
  2. g(x) = ((3 * x^(2)) + x + 12) / (x^(2) - 1)
  3. Numeric n_0(0)
  4. Numeric n_1(0)
  5. Numeric n_2(0)
  6. Numeric n_3(0)
  7. Numeric d_0(0)
  8. Numeric d_1(0)
  9. Numeric d_2(0)
  10. Numeric d_3(0)
  11. Numeric n_lead(1.4)
  12. Numeric d_{lead}(0.3)
  13. Numeric p_{lead}(7.2)
  14. Numeric q_{lead}(6.5)
  15. r(x) = (n_0 + (n_1 * x) + (n_2 * x^(2)) + (n_3 * x^(3))) / (d_0 + (d_1 * x) + (d_2 * x^(2)) + (d_3 * x^(3)))
  16. h(x) = (n_0 + (n_1 * x) + (n_2 * x^(2)) + (n_3 * x^(3)) + (n_lead * x^(p_{lead}))) / (d_0 + (d_1 * x) + (d_2 * x^(2)) + (d_3 * x^(3)) + (d_{lead} * x^(q_{lead})))