It is given a plane with a coordinate system with a beginning at the point $O$. $A(n)$, when $n$ is a natural number is a count of the points with whole coordinates which distances to $O$ are less than or equal to $n$. (a) Find $$\ell=\lim_{n\to\infty}\frac{A(n)}{n^2}.$$(b) For which $\beta$ $(1<\beta<2)$ does the following limit exist? $$\lim_{n\to\infty}\frac{A(n)-\pi n^2}{n^\beta}$$