answer 7 5. If a = 0.1 and b=1.0, how many steps of the bisection method are needed to determinethe root with an error of at most 0.5×10¯8 ?6. If the bisection method is used starting with the interval [1, 3], how many steps must betaken to compute a root accurate to 4 decimal places?7. Consider the bisection method starting with the interval [1.0. 2.5]. Find the width of theinterval at the n-th step of this method. What is the maximum distance possible between theroot and the midpoint of this interval?

Answered: Image /qna-images/answer/dde40103-9642-40f7-bc51-410c6159e6ac.jpg

Answered: 7. Consider the bisection method…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Use Bisection method to compute the root of the equation f(x) = x? — x — 1 in the interval (1,2) accurate to within &€ = 0.2% .
1. Use Bisection method to compute the root of the equation f(x) = x? — x — 1 in the interval (1,2) accurate to within & = 0.2% .
How many iteration of the bisection method are needed to achieve an accuracy of ? = 5 × 10−2 when approximating the root of the following functions.i) f(x) = x^3-x^2-x-1,[1, 2].ii) g(?) = x- cos(x), [0, 1].
Compute for the absolute relative error of the fifth iteration of bisection method in the equation x – sin(x) – 0.5 = 0 between 1 and 2.Group of answer choices 3.128% 5.128% 2.128% 4.128%
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7) The diameter of the base and the height of a closed right circular cylinder are measured,and measurements are known to have errors of at most 0.5 cm. If the diameter and height aretaken to be 4 cm and 8 cm, respectively, find bounds for the propagated error ina) the volume V of the cylinder, b) the surface area S of the cylinder.
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: Use Bisection method with initial guesses xl = 1.2 and xu = 1.5 to find the root of thefollowing (e pow -x) = x - 1 with error of significant figures(Es) = 0.5
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7. Consider the bisection method starting with the interval [1.0, 2.5]. Find the width of the interval at the n-th step of this method. What is the maximum distance possible between the root and the midpoint of this interval?