一道简单的高数题.曲面sin(xy)-2cos(yz)=0上点（派/2,1,派/3）处得切平面方程为.

Question

一道简单的高数题.
曲面sin(xy)-2cos(yz)=0上点（派/2,1,派/3）处得切平面方程为.

Answer 1

方程sin(xy)-2cos(yz)=0两端取全微分得d[sin(xy)-2cos(yz)=0]=0cos(xy)(ydx+xdy)+2sin(yz)(zdy+ydz)=0将(π/2,1,π/3)代入并将dx,dy,dz换成(x-π/2),(y-1),(z-π/3)便得切平面方程cos(π/2)[(x-π/2)+π/2(y-1)]+2si...