Hello MHF,

Needing some help with this question,

What condition must the nonnegative integers $\displaystyle m,n,p$ satisfy to guarantee that $\displaystyle \lim_{(x,y)\to(0,0)} \frac{x^my^n}{(x^2+y^2)^p}$ exists? Prove your answer. [You may assume that $\displaystyle m,n,p$ are not all zero.]