A parametrized surface is described by a differentiate function Phi: R->R. Assuming Tu times Tv not equal zero, show that the range of the linear transformation D Phi (u0, vo) is the plane spanned by Tu and Tv, are evaluated at (u0, v0).] Show that w (Tu times Tv) if and only if w is in the range of DPhi(u0, v0). Show that the tangent plane as defined in this section is the same as the "parametrized plane"
Show transcribed image text A parametrized surface is described by a differentiate function Phi: R->R. Assuming Tu times Tv not equal zero, show that the range of the linear transformation D Phi (u0, vo) is the plane spanned by Tu and Tv, are evaluated at (u0, v0).] Show that w (Tu times Tv) if and only if w is in the range of DPhi(u0, v0). Show that the tangent plane as defined in this section is the same as the "parametrized plane"