展开全部解:∵lim(x->0,y->0)[sin(xy)/(xy)] =lim(z->0)[sinz/z] (令z=xy) =1 (应用重要极限) ∴lim(x->0,y->0)[sin(xy)/x] =lim(x->0,y->0)[y*sin(xy)/(xy)] (分子分母同乘y) =[lim(x->0,y->0)y]*{lim(x->0,y->0)[sin(xy)/(xy)]} =[lim(x->0,y->0)y]*1 =lim(x->0,y->0)y =0。