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Math1023 Limit Example: Two Planes

Math1023 Limit Example: Two Planes
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2019-05-01 19:54
FunctionCoordinate GeometryCalculusLimitInequality
This example demonstrates the geometric phenomenon of two planes intersecting under the concept of limits. Core math concepts include limits, functions, inequalities, and coordinate geometry. Construction highlights involve using GeoGebra commands like f, x0, y0, δ, eps, O, L, b, c, a, z_1, A, and slider animations to illustrate the limit process, suitable for calculus and coordinate geometry learners.

GeoGebra Commands & Parameters

  1. f(x, y) = ((x^(2) * y)) / (x^(4) + y^(2))
  2. Numeric x0(0)
  3. Numeric y0(0.1)
  4. Numeric δ(1.01)
  5. Numeric eps(0.2)
  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)