Comparision of 1st, 2nd and 4th order approximation errors for a range of dx

Objective: clear all close all clc %function = sin(x)/x^3 %derivative of function = (x^3*(cos(x) - sin(x)*3*x^2)/x^3 x = pi/3; dx = linspace(pi/4,pi/4000,20); for i = 1:length(dx) [first_order_error(i), second_order_error(i), fourth_order_error(i)] = all_approximations(x,dx(i)); end figure(1) loglog(dx,first_order_error,'color','r')…