用定义域证明函数f(x)=1/1+x^2在[0,+∞)上单调递减

用定义验证函数f(x)=1/(1+x^2)在[0,+oo)上单调递减：任取y>x>=0,计算:f(y)-f(x)=1/(1+y^2)-1/(1+x^2)=[(1+x^2)-(1+y^2)]/[(1+y^2)(1+x^2)]=(x^2-y^2)/[(1+y^2)(1+x^2)]=(x-y)(x+y)/[(1+y^2)(1+x^2)]=0的任意性即知函数f(x)在[0,+oo)上单调递减