Question: Use the normal vector computed in Exercise 8 to estimate the area of the small patch of the surface (Phi(u, v)=left(u^{2}-v^{2}, u+v, u-vight)) defined by

Use the normal vector computed in Exercise 8 to estimate the area of the small patch of the surface \(\Phi(u, v)=\left(u^{2}-v^{2}, u+v, u-vight)\) defined by
\[
2 \leq u \leq 2.1, \quad 3 \leq v \leq 3.2
\]

Data From Exercise 8

Calculate \(\mathbf{T}_{u}, \mathbf{T}_{v}\), and \(\mathbf{N}(u, v)\) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point.

\(\Phi(u, v)=\left(u^{2}-v^{2}, u+v, u-vight) ; \quad u=2, \quad v=3\)

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