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Limits of Rational Functions at Infinity

Limits of Rational Functions at Infinity
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2020-07-25 02:09
FunctionCalculusLimit
This example demonstrates the behavior and limit values of rational functions at infinity. Core math concepts include limits, rational functions, polynomials, and infinity. GeoGebra commands Random, Sequence, Expand, Limit, Textfield, FractionText are used, with objects like dn, dd, cn, cd, f, g, r, lim, nlim, l, nl, button1, InputBox1, InputBox2, text3, text4, text1, text2, text5, A, B, C, D. Suitable for high school and above learning calculus and function limits.

GeoGebra Commands & Parameters

  1. Random(1, 7) → dn
  2. Random(1, 7) → dd
  3. Sequence(Random[-7, 7], k, 0, dn) → cn
  4. Sequence(Random[-7, 7], k, 0, dd) → cd
  5. Expand(Simplify[Sum[(cn(i) * x^(i - 1)), i, 1, Length[cn]]]) → f
  6. Expand(Simplify[Sum[(cd(i) * x^(i - 1)), i, 1, Length[cd]]]) → g
  7. Limit(r, Infinity) → lim
  8. Limit(r, -Infinity) → nlim
  9. Textfield(l) → InputBox1
  10. Textfield(nl) → InputBox2
  11. FractionText(l) → A
  12. FractionText(lim) → B
  13. FractionText(nl) → C
  14. FractionText(nlim) → D

AI Drawing Prompt Reference

Create a mathematical diagram illustrating the limits of a rational function at infinity. Generate two random polynomials as numerator and denominator to form a rational function. Plot the function curve in a coordinate system and indicate its horizontal asymptotes. Place two input boxes beside the graph for entering the limits as x approaches positive and negative infinity. Additionally, display the function expression and both limits in fraction form. The layout should clearly show the function graph, asymptotes, and limit values for comparison, suitable for calculus learning at high school level and above.
The prompt above was compiled from the original drawing commands and is for reference only.