Effect of dx on Error approximations

Objective: First order Approximation: % first order approximation function [error] = first_order_approximation(x,dx) analytical_derivative = (x^3*cos(x)-sin(x)*3*x^2)/(x^6); approximation_first_order = (sin(x+dx)/((x+dx)^3)-sin(x)/(x^3))/dx error = abs(approximation_first_order - analytical_derivative); end Second order Approximation:…