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One-Sided Limits

One-Sided Limits
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2017-07-15 23:28
FunctionCalculusLimit
This example demonstrates the concept of one-sided limits. It involves key mathematical concepts such as limits and functions. Using GeoGebra commands like Point, Function, Segment, Intersect, etc., the construction of one-sided limits is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Function((x - 1)^(2) / 2 + n, 1, 3.5) → g
  3. Point(g) → B
  4. Point(yAxis) → C
  5. Segment(C, D) → a
  6. Segment(B, A) → b
  7. Segment(D, A) → c
  8. Segment(E, B) → d
  9. Intersect(xAxis, yAxis) → F
  10. Ray(A, F) → e
  11. Point(xAxis) → G
  12. Ray(A, G) → h
  13. Segment(H, J) → i
  14. Segment(I, K) → j
  15. Vector(J, L) → u
  16. Vector(K, M) → v

AI Drawing Prompt Reference

Draw the graph of the function g(x) = (x - 1)²/2 + n near x=1, where n is a constant. First, draw the graph of g from x=1 to x=3.5. Then, take points A and B on the x-axis to represent the left and right limits of the function at x=1. Next, draw a perpendicular line from A to the x-axis and a line segment from A to B. Then, draw a ray from A to the y-axis and another ray from A to point G on the x-axis. Finally, draw a line segment from G to another point H on the x-axis and a line segment from H to A.
The prompt above was compiled from the original drawing commands and is for reference only.