Show that (Phi(r, theta)=left(r cos theta, r sin theta, 1-r^{2}ight)) parametrizes the paraboloid (z=1-x^{2}-y^{2}). Describe the grid
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Show that \(\Phi(r, \theta)=\left(r \cos \theta, r \sin \theta, 1-r^{2}ight)\) parametrizes the paraboloid \(z=1-x^{2}-y^{2}\). Describe the grid curves of this parametrization.
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We substitute xr cos theta and yr sin theta in the righthand side o...View the full answer
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