MathPlotAI Logo MathPlotAI

Limits at Discontinuities

Limits at Discontinuities
Loading the math board and drawing, please wait…
2020-06-15 08:54
FunctionCalculusLimit
In collections Rational Functions
This example demonstrates the limits of functions at discontinuities. Key mathematical concepts include limit theory. Using GeoGebra commands such as Root, Intersection, Length, Sequence, and Limit, discontinuous functions can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Root(Denominator[r]) → A, B, C
  2. Intersection(rootsd, rootsm) → commonroots
  3. Length(commonroots) → numberofholes
  4. Sequence(x = x(Element[commonroots, i]), i, 1, numberofholes, 1) → lines
  5. Sequence(x(Element[commonroots, i]), i, 1, numberofholes, 1) → xvals
  6. Sequence((Element[xvals, i], r(Element[xvals, i])), i, 1, numberofholes, 1) → holes
  7. Sequence(Limit[r, Element[xvals, i]], i, 1, numberofholes, 1) → list1
  8. Sequence((Element[xvals, i], Element[list1, i]), i, 1, numberofholes, 1) → list2
  9. Limit(r, Infinity) → a
  10. Limit(r, -Infinity) → b
  11. Textfield(n) → InputBox1
  12. Textfield(d) → InputBox2
  13. PartialFractions(r) → p
  14. Sequence((Element[xvals, i], Element[list1, i]), i, 1, numberofholes, 1) → l1

AI Drawing Prompt Reference

Draw a function r with discontinuities, including the roots A, B, C of the denominator, the common roots commonroots of the function, and the limit values list1 at each discontinuity. Show the limits of the function at positive and negative infinity, a and b.
The prompt above was compiled from the original drawing commands and is for reference only.