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Phantom Graph of 1/(1+x^2)

Phantom Graph of 1/(1+x^2)
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2018-07-15 09:50
FunctionCoordinate GeometryCalculusDerivativeLimit
In collections Phantom Graphs
This example demonstrates the graph of the function 1/(1+x^2), known as the standard Cauchy distribution curve. Key math concepts include function graphing, analytic geometry, and calculus concepts like limits and derivatives. It uses GeoGebra commands such as ComplexRoot, CurveCartesian, and Plane. Suitable for high school and above students to learn function plotting and properties, ideal for introductory calculus teaching.

GeoGebra Commands & Parameters

  1. ComplexRoot((c * (x^(2) + 1)) - 1) → z_1, z_2
  2. CurveCartesian(0, 1 / (1 - v^(2)), v, v, -25, 25) → a
  3. Plane((0, c, 0), (1, c, 0), (0, c, 1)) → b