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?
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?
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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answer 7
![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fb2d316-2402-4377-835d-bb3f3e603de5%2Fdde40103-9642-40f7-bc51-410c6159e6ac%2Fnbxa6l9_processed.jpeg&w=3840&q=75)
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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