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# 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)

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- MichaelLv 41 decade agoFavorite Answer
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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