Suppose that the surface S is determined by the formula z = g (x, y). Show that

Question:

Suppose that the surface S is determined by the formula z = g (x, y). Show that the surface integral in Stokes's Theorem can be written as a double integral in the following way:

Where n is the upward normal to S and Sxy is the projection of S in the xy-plane?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

See More Books

Question Posted: Jun 21, 2016 11:21 AM

See More Questions

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of...
a) Suppose that E is a two-dimensional region and that S = {(x, y, z) R3: (x, y) E and z = 0}. Prove that and that for each continuous g : E R. b) Let f : [a, b] R be a Cp function, let C be the...
Suppose that (E) is a Cp surface and that (x0, y0, z0) = (u0, v0)* where (u0, v0) E. If N (u0, v0) 0, prove that (E) has a tangent plane at (x0, y0, z0)-
What is food processing ? Different types of food processing methods Briefly explained
Ernesto Ortiz, famed American corporate raider, initiates a hostile takeover of Bundesbank Freidumia (BF), the largest commercial bank in Freidumia. In purchasing 70 percent of BFs shares, Ortiz pays...
35. Marco, Jaclyn, and Carrie formed Daxing Partnership (a calendar year-end entity) by contributing cash 10 years ago. Each partner owns an equal interest in the partnership and has an outside basis...
We posit that the relationship between age and economic peril is nonlinear, but is this relationship the same for whites and blacks? Using the ANES Economic Peril Index as your dependent variable,...
Del Spencer is the owner and founder of Del Spencers Mens Clothing Store. Del Spencers has its own house charge accounts and has found from past experience that 10 percent of its sales are for cash....
Vitex, Incorporated, manufactures a popular consumer product and it provided the following data from its standard cost system: * Applied to Work in Process during the period. The company's...
The Young Corporation has been operating successfully for several years. It is authorized to issue 24,000 shares of no-par common stock and 6,000 shares of 8%, $100 par preferred stock. The...
In Problems 1-3, use Stokes's Theorem to calculate? 1. F = x2 i + y2 j z2 k; S is the hemisphere z = (1 - x2 - y2 and n is the upper normal. 2. F = xy i + yz j + xy k; S is the triangular surface...
Let F = x2 i - 2xy j + yz2 k and S be the boundary of the surface z = xy, 0 ( x ( 1, 0 ( y ( 1, oriented counter clock wise as viewed from above. Use Stokes's Theorem and Problem 13 to evaluate or F...
A rotating light on the exterior of an aircraft is a(n) __________________ light.
Prove (11.32) . E (Yi,k | Zi = 0, = e) = E (Yi,k | i = 1, = e) = E (Yi,k | Ti = e), k = 1,2. (11.32)
University Medical Center needs to move from its existing facility to a new and larger facility five miles away from its current location. Due to construction delays, however, much of the new...
Calculate the base value or lump sum for each of the single and married filing jointly 2016 brackets given in Table 6.4. Table 6.4 ITABLE 6.4 Corporate Income Brackets and Tax Rates, 2015 Taxable...
Show that staged column diameter is proportional to (feed rate) ${ }^{1 / 2}$ and to $(1+\mathrm{L} / \mathrm{D})^{1 / 2}$.
An atmospheric column with 25 real stages is operating with a pressure drop of 0.6 in. of water per stage. Assume pressure drop in the condenser and the reboiler is $1.2 \mathrm{in}$. of water...
Have each group member make a flashcard with one of the following on the front: Hsoln , Hlattice , Hsolvent , Hmix , and Hhydration . On the back of the card, each group member should describe...
Distinguish between the work performed by public accountants and the work performed by accountants in commerce and industry and in not-for-profit organisations.
Dell Computer makes its suppliers wait 37 days on average to be paid for their goods; however, Dell is paid by its customers immediately. Thus, Dell earns interest on this float, the money that it is...
Many retirement funds charge an administrative fee equal to 0.25% on managed assets. Suppose that Alexx and Spenser each invest $5,000 in the same stock this year. Alexx invests directly and earns 5%...
Your gas-guzzling car gets only 10 miles to the gallon and has no resale value, but you are sure that it will last five years. You know that you can always buy a used car for $8,000 that gets 20...
Jen bought 100 shares of ABC stock at $15 a share on July 14, 2017. On August 7, 2018, she noticed that the stock had increased in value to $20 a share and decided to sell her shares. Jen's marginal...
Alex. Inci, buys 40 petcent of Steinbart Company on January 1, 2020, for $1.212.000. The equity method of accounting is to be used. Steinbart's net assets on that datewere $2.90 million. Any excess...
exercise 4-7 (Algo) Effects of transactions on income statement LO P2

Suppose that the surface S is determined by the formula z = g (x, y). Show that

Question:

(curl F) n dS(curl F).(gi k) dA

Step by Step Answer:

Let Hx y z z gx y 0 ...View the full answer

Calculus

Students also viewed these Calculus questions