Question
Find an equation of the tangent plane to the given parametric surface at the specified point.$ x = u + v $, $ y = 3u^2 $, $ z = u - v $; $ (2, 3, 0) $
Step 1
We can do this by solving the system of equations given by the parametric surface: \[ \begin{cases} u + v = 2 \\ 3u^2 = 3 \\ u - v = 0 \end{cases} \] From the third equation, we can see that $u = v$. Substituting this into the first equation gives $2u = 2$, so Show more…
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