(See) (a) Given a transformation coming from x=x[u, v, w], y=y[u, v, w], and z=z[u, v, w] Say how you use grad; x[u, v, w], grady;[u, v, w], and gradz;[u,

Question: (a) Given a transformation coming from

$x=x[u, v, w], y=y[u, v, w]$, and $z=z[u, v, w]$

Say how you use

$\operatorname{grad} x[u, v, w], \operatorname{grady}[u, v, w]$, and $\operatorname{gradz}[u, v, w]$

to calculate $V_{x y z}[u, v, w] \geq 0$

Then discuss the meaning of $\mathrm{V}_{\mathrm{xyz}}[\mathrm{u}, \mathrm{v}, \mathrm{w}]$

(b) Set numbers $r^{*}$, slow, shigh, tlow, and thigh so that the xyz-points

\[\begin{aligned} &\{x[s, t], y[s, t], z[s, t]\}= \\ &\quad\left\{\mathrm{r}^{*} \operatorname{Sin}[s] \operatorname{Cos}[t], r^{*} \operatorname{Sin}[s] \operatorname{Sin}[t], r^{*} \operatorname{Cos}[s]\right\} \end{aligned}\]

with slow $\leq \mathrm{s} \leq$ shigh and tlow $\leq \mathrm{t} \leq$ thigh describe the part of the sphere

\[x^{2}+y^{2}+z^{2}=4\]

consisting of those points with $x \geq 0$

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Solution: The downloadable solution consists of 1 pages
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(See) (a) Given a transformation coming from x=x[u, v, w], y=y[u, v, w], and z=z[u, v, w] Say how you use grad; x[u, v, w], grady;[u, v, w], and gradz;[u,

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