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Solved: Parametric descriptions Give a parametric
Chapter 11, Problem 12E(choose chapter or problem)
QUESTION:
Give a parametric description of the form \(\mathbf{r}(u, v)=\langle x(u, v), y(u, v), z(u, v)\rangle\) for the following surfaces. The descriptions are not unique.
The cap of the sphere \(x^{2}+y^{2}+z^{2}=16, \text { for } 4 / \sqrt{2} \leq z \leq 4\)
Questions & Answers
QUESTION:
Give a parametric description of the form \(\mathbf{r}(u, v)=\langle x(u, v), y(u, v), z(u, v)\rangle\) for the following surfaces. The descriptions are not unique.
The cap of the sphere \(x^{2}+y^{2}+z^{2}=16, \text { for } 4 / \sqrt{2} \leq z \leq 4\)
ANSWER:Solution 12E
Step 1
For a given function of the form, the gradient of such function is defined as follows: