Consider the function defined $by$

$f(x,y)=\{\begin{array}{ccc}\frac{xy}{x^2+y^2},& if(x,y)(0,& 0)\\ 0,& if(x,y)=(0,& 0)\end{array}$

$(a)$ Use the $limit\underset{h0}{lim}\frac{f(h,0)-f(0,0)}{h}to$ calculate $f_x(0,0).$

$(b)$ Use the $limit\underset{h0}{lim}\frac{f(0,h)-f(0,0)}{h}to$ calculate $f_y(0,0).$

$(c)Isf\underset{(x,y)(0,0)}{lim}f(x,y)$ and compare this

$limittof(0,0).$