illusiia
2020-11-02
Answered

Suppose that the plane region D, its boundary curve C, and the functions P and Q satisfy the hypothesis of Greens

You can still ask an expert for help

asked 2021-01-27

Proof of Stokes’ Theorem Confirm the following step in the proof of Stokes’ Theorem. If z = s(x, y) and f, g, and h are functions of x, y, and z, with M = f + hz_x and $N=g+h{z}_{y}$ , then

${M}_{y}={\u0192}_{y}+{\u0192}_{z}{z}_{y}+h{z}_{xy}+{z}_{x}(hy+{h}_{z}{z}_{y})$

and

${N}_{x}={g}_{x}+{g}_{z}{z}_{x}+h{z}_{yx}+{z}_{y}({h}_{x}+{h}_{z}{z}_{x})$ .

and

asked 2021-03-08

z = x Let be the curve of intersection of the cylinder ${x}^{2}+{y}^{2}=1$ and the plane , oriented positively when viewed from above . Let S be the inside of this curve , oriented with upward -pointing normal . Use Stokes ' Theorem to evaluate $\int ScurlF\cdot dS{\textstyle \phantom{\rule{1em}{0ex}}}\text{if}{\textstyle \phantom{\rule{1em}{0ex}}}F=yi+zj+2xk$ .

asked 2020-12-29

Use the Divergence Theorem to find the flux of $F=x{y}^{2}i+{x}^{2}yj+yk$ outward through the surface of the region enclosed by the cylinder ${x}^{2}+{y}^{2}=1$ and the planes z = 1 and z =-1.

asked 2022-02-11

* *

S is the surface of the solid bounded by the cylinder

asked 2021-01-13

How do Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem relate to the Fundamental Theorem of Calculus for ordi-nary single integral?

asked 2020-12-13

Use Greens

asked 2021-02-09

What is the Divergence Theorem? Explain how it generalizes Green’s Theorem to three dimensions.