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Example of Limit of a Function of Two Variables: Two Planes

Example of Limit of a Function of Two Variables: Two Planes
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2019-05-01 19:42
FunctionTrigonometryCoordinate GeometryLimitGraphing
This example demonstrates the calculation of the limit of a function of two variables by showing the intersection of two planes. Key mathematical concepts include functions of two variables, limits, and trigonometry. It uses GeoGebra commands such as functions, slider animation, and locus. Suitable for university-level calculus courses.

GeoGebra Commands & Parameters

  1. f(x, y) = ((x * y)) / (x^(2) + y^(2))
  2. Numeric x0(0)
  3. Numeric y0(0.1)
  4. Numeric δ(2.62)
  5. Numeric eps(0.3)
  6. (x0, y0)
  7. Numeric L(0)
  8. z = L + eps
  9. z = L - eps
  10. a(x, y) = (x - x0)^(2) + (y - y0)^(2) < δ^(1 / 2)
  11. z_1(x, y) = If[(x - x0)^(2) + (y - y0)^(2) < δ^(1 / 2), f(x, y)]
  12. (x0, y0, L)