Wurzel

Um die Wurzel aus einer Zahl im Potenzenbereich zu ziehen,
 wird ihr Exponent (Logarithmus) halbiert.
                                                      y kann variiert werden.

Erklärung

Basis = 2 (slider from 2 to 10, step 0.25)
f(x) = Basis^(x)
A = Point(yAxis)
g = Line(A, xAxis)
D = Intersect(f, g, (2.584962500597706, 5.999999999486585))
i = Line(D, yAxis)
E = Intersect(i, xAxis)
G: (x(E) / 2, 0)
k = Line(G, yAxis)
H = Intersect(f, k, (1.292481250298853, 2.4494897426783777))
l = Line(H, xAxis)
I = Intersect(l, yAxis)
p = Segment(E, D)
q = Segment(A, D)
r = Segment(I, H)
s = Segment(H, G)
Text3 = Text(x(E))
Text5 = Text(x(G))
Text6 = Text(y(I))
Text2: "y = " + (LaTeX[Basis]) + "^ x"
Text4 = Text("Exponentenbereich")
a = false
B = (0.1383043229124188, 7.595976041056748)
Text8 = VerticalText("Potenzenbereich", B)
Text1 = Text(("y = " * y(A)))
b: y(A)
c: x(E)
d: x(G)
e: y(I)
Text10: "\hspace{2ex} " + (LaTeX[b]) + " = " + (LaTeX[Basis]) + "^{ " + (LaTeX[c]) + "}    \hspace{2ex} \mid  \sqrt{}\\\\
\sqrt{" + (LaTeX[b]) + " }=\big (" + (LaTeX[Basis]) + "^{ " + (LaTeX[c]) + "} \big )^\frac{1}{2}\\\\
\hspace{4ex} =" + (LaTeX[Basis]) + "^{ " + (LaTeX[d]) + "} =  " + (LaTeX[e]) + ""
h = false
Text9: "\sqrt{" + (LaTeX[b]) + "}=" + (LaTeX[e]) + ""