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Math · Advanced Math
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I. Let f(x) = x5+2+1, and consider using the Newton-Raphson method to determine the root to this equation (a) Write down the Newton-Raphson algorithm which determines Tn+1 in terms of xn in this situation. (b) By choosing x -1, find the quantities r2, 23, . ,z1o in this instance. (Note: You can use and modify the provided Matlab codes in this instance; issuing the command x on the command line will output the elements of the vector x that you have com puted.) How many iterations seem necessary to get an answer correct to four decimal places? (c) Consider now the Newton-Raphson method for determining the solution to r3-0. Clearly the only solution to this equation is x = 0·Write down the Newton-Raphson algorithm which determines xn+1 in terms of xn In this situation. Explain with the aid of a diagram what is happening in this particular situation.

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