PLEASE WRITE THESE FUNCTIONS IN R PROGRAMMING:

fixed_point <- function(x_0, f, n = 15, tol = 0.05) { # Apply fixed point iteration to a function f. # You should start with x_0. # Return all iteration values with a vector. You should have a u vector # where u = [x_0, x_1, ..., x_n] }

newtons_method_nth_root <- function(x_0, A, n, n_iter = 15, tol = 0.05) { # Find the n-th root of number A. Use Newton's method. # f(x) = x^n - A.

}

newtons_method_root <- function(x_0, A, n_iter = 15, tol = 0.05 ) { # Write a function applying Newton's method to find the square root of # 2. You should consider the root of f(x) = x^2 - A. # n_iter is the maximum number of iterations. # tol is the solution tolerance

}