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5. If a = 0.1 and b=1.0, how many steps of the bisection method are needed to determine the root with an error of at most 0.5×1082

5. If a = 0.1 and b=1.0, how many steps of the bisection method are needed to determine the root with an error of at most 0.5×1082

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5. If a = 0.1 and b=1.0, how many steps of the bisection method are needed to determine the 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 be taken 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 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?
Transcribed Image Text:5. If a = 0.1 and b=1.0, how many steps of the bisection method are needed to determine the 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 be taken 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 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?
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