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Limit of sin(x)/x

Limit of sin(x)/x
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2019-02-24 02:42
FunctionTrigonometryLimit
This example demonstrates the limit of sin(x)/x. Key mathematical concepts include trigonometric functions and limits. Using commands such as Circle, Intersect, CircleArc, Point, Line, Polygon, CircleSector, OrthogonalLine, and Dilate, the graph of sin(x)/x can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Intersect(c, f, 1) → A
  3. Intersect(c, yAxis, 2) → B_1
  4. CircleArc(O, A, B_1) → d
  5. Point(d) → P
  6. Line(O, P) → g
  7. Intersect(f, g) → B
  8. Polygon(O, A, B) → t1, b, o, a_2
  9. CircleSector(O, A, P) → e
  10. Polygon(O, A, P) → t2, p, o_1, a_1
  11. Point(xAxis) → C
  12. OrthogonalLine(C, xAxis) → h
  13. Point(h) → D
  14. Point(h) → E
  15. Dilate(O, a, D) → O'
  16. Dilate(A, a, D) → A'
  17. Dilate(B, a, D) → B'
  18. Polygon(O', A', B') → t1', b', o', a'
  19. Dilate(e, a, E) → e'
  20. Point(h) → F
  21. Dilate(O, a, F) → O'_1
  22. Dilate(A, a, F) → A'_1
  23. Dilate(P, a, F) → P'
  24. Polygon(O'_1, A'_1, P') → t2', p', o'_1, a'_1

AI Drawing Prompt Reference

Draw the graph of sin(x)/x and demonstrate its limit as x approaches 0. Start by drawing a unit circle, then find the intersection point A between the circle and the function. Draw an arc and point P, then draw a line g through P that intersects the function at point B. Use points O, A, and B to construct polygons t1 and b, then draw a sector e with a central angle of π/2. Construct polygons t2 and p, then take point C on the x-axis and draw a perpendicular line h through C, taking points D and E on h, and use D and E to scale the original figure, resulting in new polygons t1', b', o', and a', as well as t2', p', o'_1, and a'_1.
The prompt above was compiled from the original drawing commands and is for reference only.