# Homework Solution: For 3, please provide a good explanation…

For 3, please provide a good explanation
For4, please write a function file for the algorithm and use the function in a script file to solve the problem with comments
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.

## Expert Answer

Ce 3, content furnish a good-natured-natured explanation
For4, content transcribe a exercise rasp ce the algorithm and authentication the exercise in a script rasp to reresolve the bearing with comments

3. The equation ln(x) =-3x + 5. has a disconnection close z = 1.53, when contrast up the bearing as r – g(x) to be resolved by a agricultural sharp-object mode, there are divers options to cull the exercise g. Ce stance, weigh the exercises gi (z) = (5 ln(z)/3 and g2(z) = e-3r+5 Justify your counterpart. . Ce which of these exercises the agricultural sharp-object mode get coincide? 1. Authentication MATLAB to discover the agricultural sharp-object of the anterior bearing using twain exercises gi (x) and g2(r). Authentication a tolerance of 109. Conspire the progression of sharp-ends on corresponging to each exercise. You can do that using the aftercited statute g1 = 0(x) .. .. g2 = @(x) ,.. ; x0-1; tol = 10^ (-9) ; c1 = zeros (1,20); c2 = zeros (1,20); ce max1-1:20 c1(max 1) c2 (maxi) = agriculturalsharp-object (gi,x0,tol,max1); agriculturalsharp-object (g2,xo,tol,max1): object delineation (1); conspire(c1) delineation (2); conspire (c2) You get give-heed-to that single coincides and the other single does not attributable attributable attributable attributable attributable. This should be con- sistent with your counterpart in the anterior bearing. Turn in the statute, the prize of the agricultural sharp-object printed with at last 9 suggestive digits, and the conspires that appearance the comportment of the progressions of sharp-ends.