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19. Show that x = tan^-1(x) has a solution alpha. Find an interval [a,b] containing alphasuch ythat for every x E [a,b] the iteration xn+1 = 1 + tan^-1(xn) n>=0 will converge to alpha. Calculate the first few iterates and estimate the rate of convergence.© BrainMass Inc. brainmass.com November 24, 2022, 11:57 am ad1c9bdddf
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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
Examine the function
And its graph:
This function is a continuous function, since it is the sum of continuous functions.
Thus there exist at least one ...
Newton's Method is used to estimate a root and the rate of convergence is found. The solution is detailed and well presented. The solution was given a rating of "5" by the student who originally posted the question.