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Limit of x/sin x

Limit of x/sin x
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2016-10-22 22:53
FunctionTrigonometryLimit
This example demonstrates the limit of x/sin x. Key mathematical concepts include trigonometric limits. Through constructing a semicircle, points, line segments, and intersections, the geometric meaning of the limit is illustrated. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Semicircle((0, 1), (0, -1)) → c
  2. Point(c) → P
  3. Segment((0, 0), P) → f
  4. Intersect(f, xAxis) → B_1
  5. Intersect(c, xAxis, 1) → A
  6. CircleArc(B_1, A, P) → d
  7. Angle(A, B_1, P) → α
  8. Segment(P, B) → g
  9. Segment(P, A) → h
  10. Angle(P, B_1, A) → β
  11. CircleArc(B_1, P, A) → e
  12. OrthogonalLine(A, xAxis) → j
  13. Line(B_1, P) → k
  14. Intersect(k, j) → Q
  15. Segment(P, Q) → l
  16. Segment(Q, A) → i
  17. CircleSector(B_1, A, P) → p
  18. CircleSector(B_1, P, A) → q
  19. Polygon(P, B_1, A) → poly1, s, t, b
  20. Polygon(Q, B_1, A) → poly2, a, c_1, b_2
  21. Segment(P, A) → f_1
  22. Segment(B_1, B) → g_1

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with radius 1, and mark a point P on the circle. Draw a line segment f from the origin to P, and let it intersect the x-axis at point B1. Construct an arc d connecting B1, A, and P. Mark angle α with P as the vertex and B1 and A as the sides. Draw line segments g and h from P to B1 and A, respectively. Construct angle β with P as the vertex and B1 and A as the sides. Draw an arc e connecting B1, P, and A. Draw a perpendicular line j to the x-axis through point A. Draw a line k through B1 and P, and let it intersect j at point Q. Draw line segments l from P to Q and i from Q to A. Construct sector p with B1 as the center and A and P as the boundaries. Construct sector q with B1 as the center and P and A as the boundaries. Construct triangle PAB1 and QAB1.
The prompt above was compiled from the original drawing commands and is for reference only.