√|xy|/(x^2+y^2)*sin(x^2+y^2)=√|xy|*[sin(x^2+y^2)/(x^2+y^2)]∴lim(x->+0,y->+0) √|xy|*[sin(x^2+y^2)/(x^2+y^2)]=√|0*0|*1=0lim(x->-0,y->-0) √|xy|*[sin(x^2+y^2)/(x^2+y^2)]=√|0*0|*1=0∴左中右极限存在，且都相等∴选A
