Exercise · ZW-PARAMETRIC-SURFACE-002 · ★☆☆ Basic
For \(\mathbf r(u,v)=\langle u^2v,\,u+v,\,v^3\rangle\), the vector \(\mathbf r_u\) at \((u,v)=(1,2)\) is:
Choose one option.
Show answer
- A. \(\langle 4,1,0\rangle\)
Explanation
Differentiating in \(u\): \(\mathbf r_u=\langle 2uv,\,1,\,0\rangle\), which at \((1,2)\) is \(\langle4,1,0\rangle\).
Review the concept: Parametric surface
A parametric surface is the set of points in space described by a vector function \(\mathbf r\) of two parameters \(u\) and \(v\) as they range over a region \(D\) of the plane.
\[\mathbf r(u,v)=\langle x(u,v),\,y(u,v),\,z(u,v)\rangle,\quad (u,v)\in D\]
More practice problems: parametric surface
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