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Limits At Infinity Explorer

Limits At Infinity Explorer
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2018-09-15 02:49
FunctionCoordinate GeometryCalculusLimitSlider Animation
This example demonstrates the behavior of functions at infinity and the changes in their graphs, involving core math concepts like limits, fractions, similar triangles, coordinate geometry, continuity, and median value. It uses GeoGebra commands/objects such as f, g, n_0, n_1, n_2, n_3, d_0, d_1, d_2, d_3, n_lead, d_{lead}, p_{lead}, q_{lead}, r, h for construction. Suitable for high school and above learners to understand limit theory and function properties.

GeoGebra Commands & Parameters

  1. f(x) = ((5 * x^(2)) - (7 * x)) / (x^(3) + 12)
  2. g(x) = ((3 * x^(2)) + x + 12) / (x^(2) - 1)
  3. Numeric n_0(0)
  4. Numeric n_1(0)
  5. Numeric n_2(0)
  6. Numeric n_3(0)
  7. Numeric d_0(0)
  8. Numeric d_1(0)
  9. Numeric d_2(0)
  10. Numeric d_3(0)
  11. Numeric n_lead(1.4)
  12. Numeric d_{lead}(0.3)
  13. Numeric p_{lead}(7.2)
  14. Numeric q_{lead}(6.5)
  15. r(x) = (n_0 + (n_1 * x) + (n_2 * x^(2)) + (n_3 * x^(3))) / (d_0 + (d_1 * x) + (d_2 * x^(2)) + (d_3 * x^(3)))
  16. h(x) = (n_0 + (n_1 * x) + (n_2 * x^(2)) + (n_3 * x^(3)) + (n_lead * x^(p_{lead}))) / (d_0 + (d_1 * x) + (d_2 * x^(2)) + (d_3 * x^(3)) + (d_{lead} * x^(q_{lead})))