x

u_0

f(x)

f(x) =

Aufklappen / Zuklappen

u_2

f''(x)

u_1

f'(x)

f'

f''

$f_1$

$f_2$

f''

Beispiel 3

Beispiel 4

$f_4$

$f_3$

x

Variationen

$h_1$

$h_2$

$f_5$

$h_3$

v1 = 0 (slider from -5 to 5, step 0.1)
k = 2 (slider from 1 to 2, step 0.1)
v0: ((k - 1) * 4.5)
v2: (-v0)
rahmen = 4 (slider from -5 to 5, step 0.1)
hoehe: rahmen / k
O0: (0 | v0)
O2: (0 | v2)
ex = 0.5 (slider from -5 to 5, step 0.1)
ey = 0.5 (slider from -5 to 5, step 0.1)
gx2(x) = v2
gx1(x) = v1
gx0(x) = v0
gy: x = 0
f = 1 (slider from -5 to 5, step 0.1)
c = 1 (slider from -4 to 4, step 1)
e = -2 (slider from -4 to 4, step 0.5)
f2(x) = (2 * x) - 2
f0(x) = (1 / 40 * x^(5)) + (-1 / 32 * x^(4)) + (-1 / 4 * x^(3))
f0h(x) = f0(x)
ft0(x) = (1 / k * f0h((k * x))) + v0
breite: hoehe
Rahmen0 = Polygon({O0 + (breite | (-hoehe)), O0 + (breite | hoehe), O0 + ((-breite) | hoehe), O0 + ((-breite) | (-hoehe))})
O1: (0 | v1)
Rahmen1 = Polygon({O1 + (breite | (-hoehe)), O1 + (breite | hoehe), O1 + ((-breite) | hoehe), O1 + ((-breite) | (-hoehe))})
f1(x) = (((1 / 4 * (x + 2)) * x) * (x - 3))
ft1(x) = (1 / k * f1((k * x))) + v1
Text1 = LaTeX(ft1, true, true)
Rahmen2 = Polygon({O2 + (breite | (-hoehe)), O2 + (breite | hoehe), O2 + ((-breite) | hoehe), O2 + ((-breite) | (-hoehe))})
ft2(x) = (1 / k * f2((k * x))) + v2
x0 = 0 (slider from -4 to 4, step 1)
x0_{1}: x0 / k
u0 = 4 (slider from 0 to 4, step 0.1)
xmin0 = Max({(-breite), x0_{1} - u0})
xmax0 = Min({breite, x0_{1} + u0})
fta0(x) = If[xmin0 ≤ x ≤ xmax0, If[v0 - hoehe ≤ ft0(x) ≤ v0 + hoehe, ft0(x)]]
Eingabefeld1 = Textfield(f0)
xWerte = Sequence(i / k, i, (-rahmen), rahmen, 1)
yWerte = Zip(fta0(i), i, xWerte)
punkteGraph = Sequence((xWerte(i) | yWerte(i)), i, 1, Length[xWerte])
P: (x0 / k | fta0(x0 / k))
u2 = 0 (slider from 0 to 4, step 0.1)
xmin2 = Max({(-breite), x0_{1} - u2})
xmax2 = Min({breite, x0_{1} + u2})
fta2(x) = If[xmin2 ≤ x ≤ xmax2, If[v2 - hoehe ≤ ft2(x) ≤ v2 + hoehe, ft2(x)]]
y0 = Vector(O0 + (0 | (-hoehe)), O0 + (0 | hoehe))
xAchse1 = Vector(O1 + ((-breite) | 0), O1 + (breite | 0))
y1 = Vector(O1 + (0 | (-hoehe)), O1 + (0 | hoehe))
xAchse2 = Vector(O2 + ((-breite) | 0), O2 + (breite | 0))
y2 = Vector(O2 + (0 | (-hoehe)), O2 + (0 | hoehe))
EinheitenXAchse0 = Sequence((i / k | 0 + v0), i, (-rahmen) + 1, rahmen - 1)
EinheitenYAchse0 = Sequence((0 | i / k + v0), i, (-rahmen) + 1, rahmen - 1)
EinheitenXAchse1 = Sequence((i / k | 0 + v1), i, (-rahmen) + 1, rahmen - 1)
EinheitenYAchse1 = Sequence((0 | i / k + v1), i, (-rahmen) + 1, rahmen - 1)
EinheitenXAchse2 = Sequence((i / k | 0 + v2), i, (-rahmen) + 1, rahmen - 1)
EinheitenYAchse2 = Sequence((0 | i / k + v2), i, (-rahmen) + 1, rahmen - 1)
u1 = 4 (slider from 0 to 4, step 0.1)
xmax1 = Min({breite, x0_{1} + u1})
xmin1 = Max({(-breite), x0_{1} - u1})
fta1(x) = If[xmin1 ≤ x ≤ xmax1, If[v1 - hoehe ≤ ft1(x) ≤ v1 + hoehe, ft1(x)]]
Q: (x(P) | fta1(x(P)))
R: (x(P) | fta2(x(P)))
a = true
b = true
h3(x) = x^(3)
h4(x) = (-x^(2))
h5(x) = (1 / 12 * x^(4))
h6(x) = (1 / 12 * x^(3))
xAchse0 = Vector(O0 + ((-breite) | 0), O0 + (breite | 0))
kf2: false
posKK2 = 700 (slider from -5 to 1000, step 0.1)
kL = -2 (slider from -5 to 5, step 0.1)
kR = 8 (slider from -5 to 10, step 0.1)
gl1 = Segment((x(P) | 7), (x(P) | -7))
variationen = true
t2(x) = (f2(x0) * (x - x0)) + f1(x0)
tt2(x) = (1 / k * t2((k * x))) + v1
tta2(x) = If[(-breite) ≤ x ≤ breite, If[v1 - hoehe ≤ tt2(x) ≤ v1 + hoehe, tt2(x)]]
t1(x) = (f1(x0) * (x - x0)) + f0(x0)
tt1(x) = (1 / k * t1((k * x))) + v0
h1(x) = (2 * x) + e
h2(x) = (-2 * x) + e
tta1(x) = If[(-breite) ≤ x ≤ breite, If[v0 - hoehe ≤ tt1(x) ≤ v0 + hoehe, tt1(x)]]
fi = 1
Text2: "f_" + fi + ""
gi = 1
f1a(x) = (((1 / 4 * (x + 2)) * x) * (x - 3))
f2a(x) = ((1 / 4 * (x + 2)) * (x - 3))
f3a(x) = (((1 / 8 * (x + 2)) * x^(2)) * (x - 3))
f4aI = Integral(f1a)
f1aI = Integral(f3a)
f5aI = Integral(f2a)
Text3: "h_" + gi + ""