z'x=2x,z'y=2y,所以曲面z=x²+y²在点(1,1,2)处的切平面的法向量是(2,2,-1),切平面的方程是2(x-1)+2(y-1)-(z-2)=0,即2x+2y-z-2=0,法线方程是(x-1)/2=(y-1)/2=(z-2)/(-1).