Week 3 - Discretization basics

Objective: close allclc% analytical function= sin(x)/x^3;% analytical derivative% f'(x)=(x^3*(cosx)-sin(x)*3*x^2/x^6;x=pi/3;analytical_derivative=((x^3)*(cos(x))-(sin(x)*3*(x^2)))/(x^6);% numerical derivative% forward_differencing=(f(x+dx)-f(x))/dx% central differencing = (f(x+dx) - f(x-dx))/2*dx;% fourth order approximation = (f(x-2*dx)-8f(x-dx)+8f(x+dx)-f(x+2*dx))/12*dx;dx=…