Prove the injectivity and differentiability of

x(u,v) = (u cos(v), u sin(v), $ \frac{u^2}{2}$ )

where:

u $ \epsilon$ (0,inf), v $ \epsilon$ (0,2$ \pi$ )

What I really want to prove is that (U,x) is a simple surface.

where U=(0,inf)x(0,2$ \pi$ )

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# Tag: $\frac{u^2}{2}$

## Prove the injectivity and differentiability of x(u,v) = (u cos(v), u sin(v), $\frac{u^2}{2}$)

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Prove the injectivity and differentiability of

x(u,v) = (u cos(v), u sin(v), $ \frac{u^2}{2}$ )

where:

u $ \epsilon$ (0,inf), v $ \epsilon$ (0,2$ \pi$ )

What I really want to prove is that (U,x) is a simple surface.

where U=(0,inf)x(0,2$ \pi$ )

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