高数~求切平面方程 高数 切平面方程
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\u6c42\u51faz\u5bf9x\u3001y\u7684\u504f\u5bfc\u6570\uff0cz(x)=(-y/x^2)/(1+y^2/x^2)\uff0cz(y)=(1/x)/(1+y^2/x^2)\uff0c\u628a\u70b9M0\u5750\u6807\u4ee3\u5165\uff0c\u5f97\u5e73\u9762\u7684\u6cd5\u5411\u91cf=\uff08z(x)\uff0cz(y)\uff0c-1\uff09=\uff08-1/2,1/2,-1\uff09\uff0c\u6240\u4ee5\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a(-1/2)(x-1)+(1/2)(y-1)+(-1)(z-\u03c0/4)=0
设G(x,y,z)＝F(x-y+z,xy-yz+zx)求偏导数：Gx＝Fu*1＋Fv*(y+z)，Gy=Fu*(-1)＋Fv*(x-z)，Gz=Fu*1＋Fv*(x-y)
代入x=2，y=1，z=-1，Fu=2，Fv=-3，得Gx=2，Gy=-11，Gz=-1
所以切平面的法向量是(2,-11,-1)，切平面方程是2(x-2)-11(y-1)-(z+1)=0，答案是 D
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