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Limits and Continuity Example 1 by S.S.Kaushik

Limits and Continuity Example 1 by S.S.Kaushik
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2016-06-01 23:19
FunctionCalculusLimitGeometric ConstructionSlider Animation
This example demonstrates the behavior of a function with a removable discontinuity at x=1 by allowing the user to drag sliders for variable 'a' and h approaching 0. It involves core calculus concepts like limits and continuity. Constructed using GeoGebra commands such as Segment and Intersect. Suitable for high school and above students learning calculus.

GeoGebra Commands & Parameters

  1. Segment(B, (x(B), 0)) → g
  2. Segment(C, (x(C), 0)) → i
  3. Segment(B, (0, y(B))) → j
  4. Segment(C, (0, y(C))) → k
  5. Intersect(g, xAxis) → D
  6. Intersect(i, xAxis) → E
  7. Intersect(j, yAxis) → F
  8. Intersect(k, yAxis) → G

AI Drawing Prompt Reference

Draw a function graph with a removable discontinuity at x=1. Adjust variables a and h using sliders to observe the limit behavior near x=1. First, draw the x-axis and y-axis, then mark the intersection points D, E, F, and G with the graph and axes.
The prompt above was compiled from the original drawing commands and is for reference only.