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Rootfinding for Nonlinear Equations

24. Which of the following iterations will converge to the indicated fixed point alpha (provided x_0 is sufficiently close to alpha)? If it does converge, five the order of convergence, for linear convergence, give the rate of linear convergence.

a) x_n+1 = -16 + 6x_m + 12/x_n alpha = 2
b) x_n+1 = 2/3x_n + 1/(x_n)^2 alpha = 3^1/3
c) x_n+1 = 12/(1+x_a) alpha = 3


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This solution explains how to answer the question about root finding for nonlinear equations. This solution is provided in an attached Word and PDF version.