设y=kx (k不等于0),则lim(x->0,y->0)[(x²-y²)/(x²+y²)]=lim(x->0,y->0)[(x²-kx²)/(x²+k²x²)=lim(x->0,y->0)[(1-k²)/(1+k²)
∵对于不同的k值,上式极限有不同的值
∴它的极限不存在.