haha
Lv 7
haha asked in 科學數學 · 1 decade ago

find the equations of the tang

find the equations of the tangent plane and normal line to the surface at the point.

z=(x^2)+y

(-1 , 1 , 2)

1 Answer

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  • 1 decade ago
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    let f(x, y, z) = (x^2)+y-z

    gradient f(x, y, z) = (2x, 1, -1)

    gradient f(-1, 1, 2) = (-2, 1, -1)

    a normal to the surface at the point (-1, 1, 2) is (-2, 1, -1)

    thus an equation for the tangent plane is (-2)*(x+1) + 1*(y-1) + (-1)*(z-2) = 0

    which simplifies to -2x+y-z = 1

    normal line to the surface at the point (-1, 1, 2) is (x+1) : (y-1) : (z-2) = (-2) : 1 : (-1)

    Source(s): me
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