Finite precision. Given a sufficiently smooth two$-$dimensional function $f,$ the purpose of this

exercise is to evaluate the accuracy of the quantity

$Q(h)-=\frac{f(x+h,y)+f(x-h,y)+f(x,y+h)+f(x,y-h)-4f(x,y)}{h^2}$

as an approximation of the laplacian of $f$ at $x$ and $y.$

Use Matlab $($or python$)$ to numerically determine the optimal value of h for f $($x$,$ y$)=$ sin$($x$+$y$)$ evaluated at x $=\backslash$pi $/8$ and y $=\backslash$pi $/8.$ Plot the errors.