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Concept of limits - Example y = 1/x

Concept of limits - Example y = 1/x
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2016-01-18 17:41
FunctionLimitGeometric Construction
This example demonstrates the behavior of the function y=1/x as x approaches 0, focusing on the concept of limits. Key mathematical concepts include limits, function graphing, and geometric construction. The construction involves using GeoGebra commands such as Point and CurveCartesian to create the function graph, along with coordinate systems and slider animations to observe limit behavior. Suitable for high school students or college freshmen to understand limit concepts and function analysis.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. CurveCartesian(t, y(FA1), t, 0, x(FA1)) → lh1
  3. CurveCartesian(t, y(FA1), t, x(FA1), 0) → rh1
  4. CurveCartesian(t, y(FB1), t, 0, x(FB1)) → lh2
  5. CurveCartesian(t, y(FB1), t, x(FB1), 0) → rh2
  6. CurveCartesian(x(FA1), t, t, 0, y(FA1)) → uv1
  7. CurveCartesian(x(FA1), t, t, y(FA1), 0) → lv1
  8. CurveCartesian(x(FB1), t, t, y(FB1), 0) → lv2
  9. CurveCartesian(x(FB1), t, t, 0, y(FB1)) → uv2

AI Drawing Prompt Reference

Draw the graph of the function y=1/x, showing the behavior of the function as x approaches 0, with left and right asymptotes to illustrate the concept of limits, and include vertical and horizontal auxiliary lines to observe the function's behavior near the origin.
The prompt above was compiled from the original drawing commands and is for reference only.