3. The equation ln(x) =-3x + 5. has a solution near z = 1.53, when setting up the problem as r – g(x) to be solved by a fixed point method, there are several options to choose the function g. For example, consider the functions gi (z) = (5 ln(z)/3 and g2(z) = e-3r+5 Justify your answer. . For which of these functions the fixed point method will converge? 1. Use MATLAB to find the fixed point of the previous problem using both functions gi (x) and g2(r). Use a tolerance of 109. Plot the sequence of points on corresponging to each function. You can do that using the following code g1 = 0(x) .. .. g2 = @(x) ,.. ; x0-1; tol = 10^ (-9) ; c1 = zeros (1,20); c2 = zeros (1,20); for max1-1:20 c1(max 1) c2 (maxi) = fixedpoint (gi,x0,tol,max1); fixedpoint (g2,xo,tol,max1): end figure (1); plot(c1) figure (2); plot (c2) You will notice that one converges and the other one does not. This should be con- sistent with your answer in the previous problem. Turn in the code, the value of the fixed point printed with at least 9 significant digits, and the plots that show the behavior of the sequences of points.
