(a) Consider the function f (2) = 3r –e and the interval I = [1,2).i. Determine, with appropriate reasoning, a bound for the number of iterationsneeded to achieve an approximation with an accuracy in the root of 10-3 ofa root of f (r) on I when applying the Bisection Method. If no root existson I, then write "no root exists."ii. Apply the Bisection Method to f (x) on I four times to approximate a root.If no root exists on I, then write "no root exists."

The Bisection method is used to find the root of a function with in an interval. It actually…

Consider the function f (x) 3r- e" and the interval I = [1, 2). i. Determine, with appropriate reasoning, a bound for the number of iterations needed to achieve an approximation with an accuracy in the root of 10-5 of a root of f (r) on I when applying the Bisection Method. If no root exists on I, then write "no root exists." ii. Apply the Bisection Method to f (a) on I four times to approximate a root. If no root exists on I, then write "no root exists."

Consider the function f (x) 3r- e" and the interval I = [1, 2). i. Determine, with appropriate reasoning, a bound for the number of iterations needed to achieve an approximation with an accuracy in the root of 10-5 of a root of f (r) on I when applying the Bisection Method. If no root exists on I, then write "no root exists." ii. Apply the Bisection Method to f (a) on I four times to approximate a root. If no root exists on I, then write "no root exists."

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

(a) Consider the function f (2) = 3r –e and the interval I = [1,2).
i. Determine, with appropriate reasoning, a bound for the number of iterations
needed to achieve an approximation with an accuracy in the root of 10-3 of
a root of f (r) on I when applying the Bisection Method. If no root exists
on I, then write "no root exists."
ii. Apply the Bisection Method to f (x) on I four times to approximate a root.
If no root exists on I, then write "no root exists."

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