Consider the code below that implements Newtons method and answer the following questions (a) What is the largest real root of the function studied in this problem (b) What is the criterion for convergence in terms of the value x (k) on the kth iteration (c) When I run the program with an initial guess x (0) 1 1, I get the following Explain the behavior of the error (i) near the initial guess and (ii) near the root 1 function problem3 9 2 fprintf('x t error ') 3 error abs (x log (x) x) 4 fprintf('86 9f t 86 6e ',x, error) 5 while error 10 ( 8) 6 7 8 9 end X X (x log (x) x) log(x) error abs (x log(x) x) fprintf(' 6 9f t $6 6e ',x, error)

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Question: Consider the code below that implements Newtons method and answer the following questions. (a) What is the largest real root of the function studied in

Consider the code below that implements Newton’s method and answer the following questions. $1 function problem3_9 2 fprintf('x \t error ') 3 error = abs (x+log (x) -x); 4 fprintf('86.9f \t 86.6e ',x,$

(a) What is the largest real root of the function studied in this problem?

(b) What is the criterion for convergence in terms of the value x^(k) on the kth iteration?

(c) When I run the program with an initial guess x⁽⁰⁾ = 1.1, I get the following: X error 1.100000000 9.951588e-01 11.541264556 1.668785e+01 4.718561059 2.602305e+00

3.041282127 3.414727e-01 2.734279473 1.604463e-02 2.718328446 4.661767e-05 2.718281829 3.997207e-10

Explain the behavior of the error (i) near the initial guess and (ii) near the root.

1 function problem3_9 2 fprintf('x \t error ') 3 error = abs (x+log (x) -x); 4 fprintf('86.9f \t 86.6e ',x, error) 5 while error > 10^(-8) 6 7 8 9 end X = X - (x+log (x) -x) /log(x); error = abs (x* log(x) -x); fprintf('%6.9f \t $6.6e ',x, error)

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