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Math Help - Calc 3, finding level sets of a function

  1. #1
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    Calc 3, finding level sets of a function

    Find all level sets of the function:

    f(x,y,z) = x^2 + y^2 - z^2



    Help please!
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  2. #2
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    If \lambda\in\mathbb{R} is a fixed number, the level sets of f:\mathbb{R}^3 \to \mathbb{R},\;\;f(x,y,z)=x^2+y^2-z^2 at level \lambda consists of all points in \mathbb{R}^3 which are solution of the equation f(x,y,z)=\lambda. If \lambda=0 the level surface is a cone centered at the origin opening along the z axis. If \lambda>0, then the level surface is a hyperboloid of one sheet. Finally, if \lambda < 0, the level surface is a hyperboloid of two sheets.
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