令y=x,lim(x,y)趋于(0,0)xy/x+y
=lim(x趋于0)x^2/(2x)=0
令y=x^2-x,lim(x,y)趋于(0,0)xy/x+y
= lim(x趋于0) x^3-x^2/ x^2 =-1
两种情况极限值不同,故原极限不存在