Bisection method

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Problem 1.23.36 from Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. "Предел. Непрерывность. Дифференцируемость." [ККЧ+03]More problems in Subsection 1.23.2 "Problems"

Using the bisection method, solve the equation with the indicated error Δ\Delta:

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(1)

x4+x−10=0,Δ=10−2x^{4}+x-10 = 0, \Delta = 10^{-2};

(2)

x3−12x−8=0,Δ=10−2x^{3}-12 x-8 = 0, \Delta = 10^{-2}

(3)

x3+x2−5x−12=0,Δ=10−2x^{3}+x^{2}-5 x-12 = 0, \Delta = 10^{-2}

(4)

x4+2x3+6x2−1=0,Δ=10−3x^{4}+2 x^{3}+6 x^{2}-1 = 0, \Delta = 10^{-3}

(5)

x4−2x3+x−1=0,Δ=10−3x^{4}-2 x^{3}+x-1 = 0, \Delta = 10^{-3};

(6)

(x−1)2−2sin⁡x=0,Δ=10−2(x-1)^{2}-2 \sin x = 0, \Delta = 10^{-2};

(7)

ex=2(1−x)2,Δ=10−2e^{x} = 2(1-x)^{2}, \Delta = 10^{-2};

(8)

10(x−1)=sin⁡x,Δ=10−310(x-1) = \sin x, \Delta = 10^{-3};

(9)

10ln⁡x=x3−3,Δ=10−310 \ln x = x^{3}-3, \Delta = 10^{-3};

(10)

xex=1,Δ=10−3x e^{x} = 1, \Delta = 10^{-3}.

Problem 1.23.38 from Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. "Предел. Непрерывность. Дифференцируемость." [ККЧ+03]More problems in Subsection 1.23.2 "Problems"

Using the graphs of the hyperbolas xy=y+1xy = y+1 and x2−y2=1x^{2}-y^{2} = 1 and the bisection method, compute with an error of 0.01 the coordinates of the points of intersection of these hyperbolas.

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Problem 1.23.50 from Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. "Предел. Непрерывность. Дифференцируемость." [ККЧ+03]More problems in Subsection 1.23.2 "Problems"

Solve the equation x3+1,1x2+0,9x−1,4=0x^{3}+1,1 x^{2}+0,9 x-1,4 = 0:

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(1)

using the bisection method to an accuracy of 5⋅10−35 \cdot 10^{-3};

(2)

using the method of chords to an accuracy of 5⋅10−45 \cdot 10^{-4};

(3)

using the method of tangents to an accuracy of 5⋅10−45 \cdot 10^{-4}.

Problem 1.23.58 from Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. "Предел. Непрерывность. Дифференцируемость." [ККЧ+03]More problems in Subsection 1.23.2 "Problems"

Solve the equation x3−4,1x2+6,1x−1,6=0x^{3}-4,1 x^{2}+6,1 x-1,6 = 0:

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(1)

using the bisection method to an accuracy of 5⋅10−35 \cdot 10^{-3};

(2)

using the method of chords to an accuracy of 5⋅10−45 \cdot 10^{-4};

(3)

using the method of tangents to an accuracy of 5⋅10−45 \cdot 10^{-4};

(4)

using the combined method to an accuracy of 5⋅10−45 \cdot 10^{-4}.

References

[ККЧ+03] Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. Предел. Непрерывность. Дифференцируемость. 2-е изд., ФИЗМАТЛИТ, 2003.