Use Matlab

Create a diary file called "lab5.txt." The function sin(x) has a fixed point of 0. Start with an initial guess of 2 and use the method of fixed point iteration to derive this fixed point. Why do you think this algorithm is converging so slowly? If you want to find a root of f(x), then f(x) = 0 f(x) + x = x This means you can always try fixed point iteration to try and find a root of function. Use the method of fixed point iteration to find roots of the following functions on the given intervals. sin (x), [-5, 5]. In(x), (0, 2) -ln(x), (0.2) The golden ratio is the positive solution to the equation x^2 - x - 1 = 0. Use Newton's Method to find the golden ratio. Newton's Method is an open root finding method that uses the following formula. When Newton's Method works, the sequence {x_n} converges to a root of f(x). x_n+ 1 = x_n - f(x)/f'(x) Use Newton's Method with f(x) = sin(x) to estimate pi. Use an initial of 3. Turn the diary file off and upload "lab5.txt" to Canvas