Let $,f$:$R^{2}R$ be the function defined by

$f(x,y)=\{\begin{array}{ccc}\frac{3y^5-x^5}{x^4+y^4},& if(x,y)(0,& 0)\\ 0,& if(x,y)=(0,& 0)\end{array}$

a$.$ Show that the function $f(x,y)$ is continuous at the point $(0,0).$

b$.$ Determine whether or not the function $f(x,y)$ is uniformly continuous on the set: $D=\{(x,y)in{R}^2$: Justify your answer.