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Function Convergence and Continuity

Function Convergence and Continuity
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2014-09-09 11:54
FunctionCalculusLimitGeometric Construction
This example demonstrates the ε-δ definition of limit in functions. Key math concepts include limits, continuity, and the ε-δ definition. It uses GeoGebra commands like If, Textfield, Vector, Line, Polygon to dynamically illustrate the changes in ε and δ, explaining the limit definition. Suitable for high school students and beginners in calculus learning the concepts of function limits and continuity.

GeoGebra Commands & Parameters

  1. If(limMode, L1, L2) → L
  2. Textfield(f) → fInput
  3. Vector(LPoint, (x(LPoint), L + epsilon)) → epsilonVector
  4. Vector(LPoint, (x(LPoint), L - epsilon)) → epsilonVector2
  5. Line(Lpoint1, Lpoint2) → LLine
  6. Line(Xpoint1, Xpoint2) → XLine
  7. Line(epsTopPoint1, epsTopPoint2) → epsilonTopLine
  8. Line(epsBottomPoint1, epsBottomPoint2) → epsilonBottomLine
  9. Polygon((viewLeft, L + epsilon), (viewRight, L + epsilon), (viewRight, L - epsilon), (viewLeft, L - epsilon)) → epsilonRegion, a, b, c, e
  10. Line(deltaLeftPoint1, deltaLeftPoint2) → deltaLeftLine
  11. Line(deltaRightPoint1, deltaRightPoint2) → deltaRightLine
  12. Vector(XPoint, (X + delta, 0)) → deltaVector
  13. Vector(XPoint, (X - delta, 0)) → deltaVector2
  14. Polygon((X - delta, viewTop), (X + delta, viewTop), (X + delta, viewBottom), (X - delta, viewBottom)) → deltaRegion, g, h, i, j
  15. Textfield(X) → XInput
  16. Line((0, L2), (1, L2)) → L2Line
  17. Textfield(L1) → Linput
  18. Polygon(Corner[1], Corner[2], (0.85 * Corner[2]) + (0.15 * Corner[3]), (0.85 * Corner[1]) + (0.15 * Corner[4])) → poly1, k, l, m, n