6. If the bisection algorithm is applied to a continuous function f(x) on an interval [a, b], where f(a) f(b) <0, then after n steps, an approximate root will have been computed with error of at most (A) (b-a)/2+1 (B)1/27/2 (C) (b-a)/22n (D)2n+1/(b-a).
6. If the bisection algorithm is applied to a continuous function f(x) on an interval [a, b], where f(a) f(b) <0, then after n steps, an approximate root will have been computed with error of at most (A) (b-a)/2+1 (B)1/27/2 (C) (b-a)/22n (D)2n+1/(b-a).
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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Question
![6. If the bisection algorithm is applied to a continuous function f(x) on an interval [a, b], where
f(a) f(b) < 0, then after n steps, an approximate root will have been computed with error of at most
-
(A) (b − a)/2n+1
(B)1/27/2
(C) (b − a)/2²n
-
(D)2n+¹/(b − a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdd460cb-04be-4962-8050-7a535e5d7a2f%2F1f937b1f-91e2-4b1b-9e06-effed8c4bda4%2Fu72zdl9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. If the bisection algorithm is applied to a continuous function f(x) on an interval [a, b], where
f(a) f(b) < 0, then after n steps, an approximate root will have been computed with error of at most
-
(A) (b − a)/2n+1
(B)1/27/2
(C) (b − a)/2²n
-
(D)2n+¹/(b − a).
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