The problem from Differential Geometry:(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]\gamma : R -> R[/tex] is smooth function and [tex]U = {(x,y,z) \in R^3 : x \ne 0}[/tex] - open subset.

Function [tex]f : U -> R[/tex] is defined as [tex]f(x,y,z) = z - x\gamma(y/x)[/tex] and this is smooth function.

Proof that for surface[tex]S = f^{-1}(0)[/tex] all tangent planes passing through coordinates origin.

Can anyone give me a hint?

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# Homework Help: Tangent planes passing through coordinates origin.

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