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Math Help - Tangent Plane Problem

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    13

    Tangent Plane Problem

    I have got stuck on finding the equation for the tangent plane for the equation:

    yz = ln(x + z), at point (0, 0, 1).

    What I have done is rearrange to

    [ ln(x + z) ]/yz = 1, then

    Fx(x, y, z) = 1/yz(x + z),

    Fx(x, y, z) = 1/(xyz + yz^2)

    Which I am pretty sure is right.

    When it comes to sub in the x = 0, y = 0, z = 1, I get this.

    1/(0 + 0), which is undefined.

    What does this mean?

    Cheers,

    Chris
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  2. #2
    Senior Member
    Joined
    Feb 2010
    Posts
    422
    Differentiate with respect to y: yz_y+z={z_y\over x+z}; and to x: yz_x = {1+z_x\over x+z} . Plug in your point to get respectively z_y=1 and z_x=-1. Technically you still have to show that z is differentiable at (0,0,1), but glossing that over, you have that the tangent plane is z-1=y-x.
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