[微分] 基本問題
Find the normal line for the surface
z = x^2-xy-y^2
at the point (1,1,-1)
好像是這樣算...
f(x,y,z) = (x^2-xy-y^2-z)
del f = <2x-y,-x-2y,-1>
|
del f | x-1 y-1 z+1
|(1,1,-1) => <1,-3,-1> =>------ = ------ = ------ = t
1 -3 -1
x = t+1
y = -3t+1
z = -t-1
------------------------------------------------------------------------
這樣算好像不行....
dz = 2xdx-ydy-xdy-2ydy
dy/dx =(2x-y)/(x+2y) 代(1,1,-1)
m=-3
=> 3x+y=4
--------------------------------------------------------------------------
我想問這題一定要用向量解嗎?!
然後我下面那解法好像錯了...
可以解釋一下嗎?!
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