Answered: (c) Given f: R → R, suppose that f is… | bartleby

Algebra & Trigonometry with Analytic Geometry

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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Please please do only number c

(a) Given f (x)
determine the minimum number of iterations required to have an accuracy of
10-9 in the root. If no root exists on the interval, then write “No root exists."
COS x
xe" on [0, 1], with reference to the Bisection Method,
||
(b) Given f (x)
f on [0, 1], accurate to 3 decimal digits. If no root exists on the interval, then
= cos x – xe", use the Bisection Method to approximate a root of
write "No root exists."
(c) Given f: R → R, suppose that f is differentiable and |f' (x)| < 1 for all x E R.
Show that the sequence generated by the fixed point iteration method applied
to f converges to a fixed point of f for any initial xo E R.
(d) Apply the fixed point iteration to sin x – x = -1 four times, with xo = ;. Use
an 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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3. The function f(x) = xe=^(-x) has a unique root x = 0.(a) Compute several iterations of the Newton's method, and conclude that the methoddoes not succeed if x_0 > 1.(b) Draw graphs to illustrate the rst few iteration when x_0 = 0.5 and x_0 = 1.5.
Use (a) Fixed Point Iteration method (b) Newton-Rhapson method and (c) Secant Method to find the solution to the following within error of 10-6. Prepare an Excel file for the finding the root until the error is within 10-6 showing also the graph of the function. sin x - e-x=0, when x = [0,1]
Determine the real root of f (x) = f (x) = 2x3-11.7x2 + 17.7x - 5a) Fixed-point iteration method (three iterations, x0 = 3). Note: Makecertain that you develop a solution that converges on the root.b) Newton-Raphson method (three iterations, x0 = 3).c) Secant method (three iterations, x-1 = 3, x0 = 4).
1. The seventh iteration k=6 of the secant method in solving the equation f(x) = x3-5x+3 resulted in x8 = 1.8249 and x7 = 1.8889. compute the next three iterations correct to 4 decimal points.
Use (a) Fixed Point Iteration method (b) Newton-Rhapson method and (c) Secant Method to find the solution to the following within error of 10-6. Show your manual solution for first three iterations, then prepare an Excel file for the finding the root until the error is within 10-6 showing also the graph of the function. x3-2x2-5=0, when x = [1, 4] sin x - e-x=0, when x = [0,1] (x-2)2-ln x =0, when x = [1,2]
The function g( x ) = π + 0.5sin(x/2 ) has a unique fixed point on [0 , 2π]. Estimate number of iterations needed to achieve an accuracy 10-7 , if we start with an initial guess Xo = π.
Use (a) Fixed Point Iteration method (b) Newton-Rhapson method and (c) Secant Method to find the solution to the following within error of 10-6. Show your manual solution for first three iterations, then prepare an Excel file for the finding the root until the error is within 10-6 showing also the graph of the function. (x-2)2-ln x =0, when x = [1,2]
The equation f (x) = 2 − x2 sin x = 0 has a solution in the interval [-1,2]. Verify that the Bisection method can be applied to the function f (x) on [-1,2]. Using the error formula for the Bisection method find the number of iterations needed for accuracy 000001. Do not do the Bisection calculations. Compute p3 for the Bisection
Use (a) Fixed Point Iteration method (b) Newton-Rhapson method and (c) Secant Method to find the solution to the following within error of 10-6. Show your manual solution for first three iterations, then prepare an Excel file for the finding the root until the error is within 10-6 showing also the graph of the function. sin x - e-x=0, when x = [0,1]
Determine the positive real root of ln(x2)=0.7 a. graphically b. using three iterations of the bisection method, with initial guesses of xl=0.5 and xu=2 c. using three iterations of the false position method, with the same initial guesses of xl=0.5 and xu=2
Use a fixed-point iteration method to determine a solution accurate to within 10−2 for 2x*cos(2x) - (x+1)^2 = 0, forx in [-1, 0]. Use p0 = 1
Answer the following within 10-5. Using the method that used in the images. 1. Use Fixed-point iteration method to solve sin x - e-x = 0, [0, 1].

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