(a) Given f (x) = x-e* on [0, 1], with reference to the Bisection Method, determinethe minimum number of iterations required to have an accuracy of 10-9 in theroot. If no root exists on the interval, then write "No root exists."(b) Given f (x) = x – e=", use the Bisection Method to approximate a root of f on[0, 1], accurate to 4 decimal digits. If no root exists on the interval, then write"No root exists."(c) Given f: R → R, suppose that f is differentiable and |f' (x)| < 1 for all r € R.Show that the sequence generated by the fixed point iteration method appliedto f converges to a fixed point of f for any initial roER.(d) Apply the fixed point iteration to cos a – x = -1 four times, with xo = }. Usean accuracy of 6 decimal digits throughout.(e) Determine if the fixed point iteration applied in the previous question will con-verge.

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Answered: (b) Given f (x) = x – e-², use the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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(b) Given f (x) = x – e-², use the Bisection Method to approximate a root of f on [0, 1], accurate to 4 decimal digits. If no root exists on the interval, then write "No root exists."