求曲面xy+yz+zx=1上点(1,-2,-3)处的切平面方程

问题描述:

求曲面xy+yz+zx=1上点(1,-2,-3)处的切平面方程

可用偏导数来求解.F(x,y,z)=xy+yz+zx-1,Fx(X,Y,Z)=y+z(对x求偏导数),Fy(X,Y,Z)=x+z(对y求偏导数),Fz(X,Y,Z)=y+x(对z求偏导数),在点(1,-2,-3)处有Fx(X,Y,Z)=-5,Fy(X,Y,Z)=-2,Fz(X,Y,Z)=-1.则在此...