FIXED POINT ITERATION plz give complete and correct answer 2

FIXED POINT ITERATION

plz give complete and correct answer

2. Use the fixed point iteration to find the solution of 3 - e\" on [1,2 correct to roughly within 10-3. Using the exact solution, find the absolute error. (Hint: Use the correct g for f(x)-3-ez and 20 = 1.5) 3. Find n for which the nth iteration by the fixed point iteration guarantees to approxi- mate the root of f(x)-x-cos x on [0, ] with accuracy within 10-1, using x,-/4.

Solution

Given 3x = e^x

consider g(x) = x = e^x /3 and the fixed point iterative scheme x_i = e^xi /3 , i = 0,1,2,3,.....

Let the intial guess be x₀ = 1/3

i 0 1 2 3 4 5

x_{i 0.33 2.463 18.294 23.356 34.653 47.346}