Ràcord Function

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2019-03-18 17:31

Function Integral Limit

This is an interesting function that demonstrates the properties of functions. The example involves core mathematical concepts such as polynomial functions, limits, and integrals. Using GeoGebra commands like Surface, CurveCartesian, Mirror, Intersect, and If, complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

Surface(t, s, sqrt((1 - (t^(2) * s^(2))) / (t^(2) + s^(2))), t, (-l1), l1, s, (-l2), l2) → a
CurveCartesian(a(t, l2), t, (-l1), l1) → b
CurveCartesian(a(l1, t), t, (-l2), l2) → c
CurveCartesian(a(t, (-l2)), t, (-l1), l1) → d
CurveCartesian(a((-l1), t), t, (-l2), l2) → e
Surface(t, p(s), q(s), t, (-l1), l1, s, (-l2), l2) → l
Surface(r(u), v, s(u), u, (-l1), l1, v, (-l2), l2) → m
Mirror(a, xOyPlane) → a'
Mirror(l, xOyPlane) → l'
Mirror(m, xOyPlane) → m'
Mirror(b, xOyPlane) → b'
Mirror(c, xOyPlane) → c'
Mirror(d, xOyPlane) → d'
Mirror(e, xOyPlane) → e'
Intersect(f, n, (-0.3523110414637638, 0.6600000010612497)) → A
Mirror(A, yAxis) → A'
If(Defined[A'], ff, f) → fff
CurveCartesian(t, fff(t), k, t, (-l1), 0) → g
CurveCartesian(t, (-fff(t)), k, t, (-l1), 0) → h
Mirror(g, i) → g_1
Mirror(h, i) → h_1
Mirror(g, xOyPlane) → g_2
Mirror(h, xOyPlane) → h_3
Mirror(h_1, xOyPlane) → h_2
Mirror(g_1, xOyPlane) → g_3

AI Drawing Prompt Reference

Draw a complex function graph, including multiple surfaces and curves. First, draw a surface, then generate multiple symmetric surfaces and curves through mirroring and intersection operations. Finally, generate the final graph through mirroring and intersection operations, demonstrating the properties of functions, including limits and integrals.

The prompt above was compiled from the original drawing commands and is for reference only.