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F(x, y, z) = 0 f(x, y, z) =

  1. Jul 3, 2010 #1
    f(x, y, z) = 0 f(x, y, z) = ....

    1. The problem statement, all variables and given/known data

    [PLAIN]http://www.netbookolik.com/wp-content/uploads/2010/07/q12.png [Broken]

    2. Relevant equations

    3. The attempt at a solution

    Sorry have no idea:(
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 3, 2010 #2


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    Re: f(x, y, z) = 0 f(x, y, z) = ....

    If a surface is given by f(x,y,z)= 0 (or any constant) we can think of it as a "level surface" so [itex]\nabla f= f_x\vec{i}+ f_y\vec{j}+ f_z\vec{k}[/itex] is normal to the surface. The tangent plane at [itex](x_0,y_0,z_0)[/itex] is of the form [itex]f_x(x_0,y_0,z_0)(x- x_0)+[/itex][itex] f_y(x_0,y_0,z_0)(y-y_0)+ f_z(x_0,y_0, z_0)(z- z_0)= 0[/itex].

    For what [itex](x_0, y_0, z_0)[/itex] does (0, 0, 0) lie on that tangent plane?
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