Show that (Phi(u, v)=(2 u+1, u-v, 3 u+v)) parametrizes the plane (2 x-y-z=2). Then (a) Calculate (mathbf{T}_{u},
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Show that \(\Phi(u, v)=(2 u+1, u-v, 3 u+v)\) parametrizes the plane \(2 x-y-z=2\). Then
(a) Calculate \(\mathbf{T}_{u}, \mathbf{T}_{v}\), and \(\mathbf{N}(u, v)\).
(b) Find the area of \(\mathcal{S}=\Phi(\mathcal{D})\), where
\(\mathcal{D}=\{(u, v): 0 \leq u \leq 2,0 \leq v \leq 1\}\).
(c) Express \(f(x, y, z)=y z\) in terms of \(u\) and \(v\), and evaluate \(\iint_{\mathcal{S}} f(x, y, z) d S\).
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We show that x2 u1 yuv and z3 uv satisfy the equation of the plane 2 xyz22 u1uv3 uv4 u2uv3 uv2 Moreo...View the full answer
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