Näherungslösung

a

b

x_m

f(x) = x^(3.0) - 2.0 * x^(2.0) + 2.0
A = Point(xAxis)
B = Point(xAxis)
A2: x(A)
B2: x(B)
n = 4 (slider from 1 to 20, step 1)
C2: (A2 + B2) / 2.0
A3 = If(f(A2) * f(C2) > 0.0, C2, A2)
B3 = If(f(B2) * f(C2) > 0.0, C2, B2)
C3: (A3 + B3) / 2.0
A4 = If(f(A3) * f(C3) > 0.0, C3, A3)
B4 = If(f(B3) * f(C3) > 0.0, C3, B3)
C4: (A4 + B4) / 2.0
A5 = If(f(A4) * f(C4) > 0.0, C4, A4)
B5 = If(f(B4) * f(C4) > 0.0, C4, B4)
C5: (A5 + B5) / 2.0
A6 = If(f(A5) * f(C5) > 0.0, C5, A5)
B6 = If(f(B5) * f(C5) > 0.0, C5, B5)
C6: (A6 + B6) / 2.0
A7 = If(f(A6) * f(C6) > 0.0, C6, A6)
B7 = If(f(B6) * f(C6) > 0.0, C6, B6)
C7: (A7 + B7) / 2.0
A8 = If(f(A7) * f(C7) > 0.0, C7, A7)
B8 = If(f(B7) * f(C7) > 0.0, C7, B7)
C8: (A8 + B8) / 2.0
A9 = If(f(A8) * f(C8) > 0.0, C8, A8)
B9 = If(f(B8) * f(C8) > 0.0, C8, B8)
C9: (A9 + B9) / 2.0
A10 = If(f(A9) * f(C9) > 0.0, C9, A9)
B10 = If(f(B9) * f(C9) > 0.0, C9, B9)
C10: (A10 + B10) / 2.0
A11 = If(f(A10) * f(C10) > 0.0, C10, A10)
B11 = If(f(B10) * f(C10) > 0.0, C10, B10)
C11: (A11 + B11) / 2.0
A12 = If(f(A11) * f(C11) > 0.0, C11, A11)
B12 = If(f(B11) * f(C11) > 0.0, C11, B11)
C12: (A12 + B12) / 2.0
A13 = If(f(A12) * f(C12) > 0.0, C12, A12)
B13 = If(f(B12) * f(C12) > 0.0, C12, B12)
C13: (A13 + B13) / 2.0
A14 = If(f(A13) * f(C13) > 0.0, C13, A13)
B14 = If(f(B13) * f(C13) > 0.0, C13, B13)
C14: (A14 + B14) / 2.0
A15 = If(f(A14) * f(C14) > 0.0, C14, A14)
B15 = If(f(B14) * f(C14) > 0.0, C14, B14)
C15: (A15 + B15) / 2.0
A16 = If(f(A15) * f(C15) > 0.0, C15, A15)
B16 = If(f(B15) * f(C15) > 0.0, C15, B15)
C16: (A16 + B16) / 2.0
A17 = If(f(A16) * f(C16) > 0.0, C16, A16)
B17 = If(f(B16) * f(C16) > 0.0, C16, B16)
C17: (A17 + B17) / 2.0
A18 = If(f(A17) * f(C17) > 0.0, C17, A17)
B18 = If(f(B17) * f(C17) > 0.0, C17, B17)
C18: (A18 + B18) / 2.0
A19 = If(f(A18) * f(C18) > 0.0, C18, A18)
B19 = If(f(B18) * f(C18) > 0.0, C18, B18)
C19: (A19 + B19) / 2.0
A20 = If(f(A19) * f(C19) > 0.0, C19, A19)
B20 = If(f(B19) * f(C19) > 0.0, C19, B19)
C20: (A20 + B20) / 2.0
A21 = If(f(A20) * f(C20) > 0.0, C20, A20)
B21 = If(f(B20) * f(C20) > 0.0, C20, B20)
C21: (A21 + B21) / 2.0
L_1: {A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21}
L_2: {B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13, B14, B15, B16, B17, B18, B19, B20, B21}
Liste1 = Sequence((Element[L_1, i], 0.0), i, 2.0, n)
Liste2 = Sequence((Element[L_2, i], 0.0), i, 2.0, n)
a = Integral(f(x), Element[L_1, n], Element[L_2, n])
L_3: {C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15, C16, C17, C18, C19, C20, C21}
Text1: "x \approx  " + (Element[L_3, n])
u = Vector((Element[L_3, n], 3.0), (Element[L_3, n], 0.0))
P: (Element[L_3, n], 0.0)
Q: P - 1.2 * u