Suggested languages for you:

Americas

Europe

Q. 20

Expert-verifiedFound in: Page 1119

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Give a formula for a normal vector to the surface S determined by y = g(x,z), where g(x,z) is a function with continuous partial derivatives.

$\mathrm{Therefore}\mathrm{the}\mathrm{required}\mathrm{normal}\mathrm{vector}\mathrm{is}=-{g}_{x}\mathbf{i}+\mathbf{j}-{g}_{z}\mathbf{k}.$

g(x, z) is a function with continuous partial derivatives.

$Byabovesteps,thesurfaceSisparametrizedbyasfollows\phantom{\rule{0ex}{0ex}}r(x,z)=>">g(x,z),x,z$

$\begin{array}{r}\mathbf{n}={\mathbf{r}}_{z}\times {\mathbf{r}}_{x}\\ =>"\; separators="|">0,{g}_{z},1& \times >"\; separators="|">1,{g}_{x},0\end{array}$

94% of StudySmarter users get better grades.

Sign up for free