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5. Assume Newton’s method is used to estimate the roots of f (x) = (x −...

5. Assume Newton’s method is used to estimate the roots of f (x) = (x − 1)2 ln x.
(a) Show that there is a cubic root
(b) Find the order of convergence
(c) Find the asymptotic error constant

its numerical methods course, there is newton method and thats the function
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5) f(n) = (x-1)? In (x). vc f(x) = 2(x-1) 10(X) + (x - 1)? a)x= is 2007 of f(n)=0 f(1) = 0 if(1) = 0 f(n) = 21n1n) + 2(x-1)- in b) 494) = xn- I lyn) flin) Xn+1 = xm- (Xn-1)? In cxn) 2{Xn-1) InLXn) + (Xn-1)2 X971-1 = xmnr) - (xn-1) In Lxn) 2in(x)ir=1; Order of convergence 1. c) c = lim | Noti- l Hannil no

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