= It is given that a sequence of Newton iterates converge to a root r of the function f(x). Further, it is given that the root r is a root of multiplicity 2, i.e., f(x) = = (x − r)² g(x), where g(r) 0. It is also given that the function f, its derivatives till the second order are continuous in the neighbourhood of the root r. If en is the error of the nth iterate, i.e., en = n - r, then obtain en+1 lim n→∞ en

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
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Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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It is given that a sequence of Newton iterates converge to a root r of the function f(x). Further,
it is given that the root r is a root of multiplicity 2, i.e., f(x) = (x – r)² g(x), where g(r) + 0. It is also
given that the function f, its derivatives till the second order are continuous in the neighbourhood of the
root r. If en is the error of the nth iterate, i.e., en = xn – r, then obtain
en+1
lim
n-00
en
Transcribed Image Text:It is given that a sequence of Newton iterates converge to a root r of the function f(x). Further, it is given that the root r is a root of multiplicity 2, i.e., f(x) = (x – r)² g(x), where g(r) + 0. It is also given that the function f, its derivatives till the second order are continuous in the neighbourhood of the root r. If en is the error of the nth iterate, i.e., en = xn – r, then obtain en+1 lim n-00 en
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