Hint: Use https://www.desmos.com/calculator or www.geogebra.org to sketch figure.1) Verify Stoke's Theorem for the vector field F(x, y, z) = 2zų + 3x] + 5yk, taking S to bethe portion of the paraboloid z = 4 – x² – y² for which z > 0 with upward orientation, and Cto be the positively oriented circle x2 + y2= 4 that forms the boundary of S in the xy - plane.Ans: 12nCS CamScanner - Wgo gaall

Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Answered: 1) Verify Stoke's Theorem for the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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8. Use (a) parametrization; (b) Stokes' Theorem to compute fF.dr for the vector field F = (x²+z)i + (y² + 2x)j + (z² −y)k and the curve C which is the intersection of the sphere x² + y² +2²=1 with the cone z = √² + y² in the counterclockwise direction as viewed from above. -
Sketch the vector field F. O F(x, y) = - − ²¹ = 1 + ( y − x) - y
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Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. The following table shows the closing prices on September 22, 2015, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day. Tech Stocks Close Change AAPL (Apple) $113.40 -1.81 ADBE (Adobe Systems) $84.66 1.34 EBAY (eBay) $25.61 -0.31 MSFT (Microsoft) $3.90 -0.21 S (Sprint) $4.40 0.02 WIFI (Boingo Wireless) $8.51 0.56 Non-Tech Stocks ANF (Abercrombie & Fitch) $21.81 -0.02 в (Воeing) $133.99 -2.03 F (Ford Motor Co.) $13.91 -0.40 GE (General Electric) $25.10 0.01 GIS (General Mills) $57.12 0.33 JNJ (Johnson & Johnson) $93.26 0.13 On the morning of September 22, 2015, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. (a) How many possible collections are possible?…
Use the method of undetermined coefficients to determine the form of a particular solution for the given equation. y'"' + 10y" – 11y=xe* + 4x What is the form of the particular solution with undetermined coefficients? Yp(x) = ] (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)
3) Compute the curl of F= (4 xy) i + (2x² + 2z²) j + (4 yz) k.
Verify Green's theorem for a vector field F(x, y) = y²³i+z²j and a triangle bounded by the lines z + y = 1 and -z+y = 1 and y= = 0. (Hint: all the conditions in the Green theorem must be verified.)
EXERCISES 2.11 1. Use Gauss's Theorem to evaluate fF.ds for the vector field, E = x³ į+ y³ į+z³k, taking S S to be a portion of the paraboloid z=4-x² - y² and plane z=0 with outward orientation.
In Cartesian coordinates, a vector field takes the form F= 2xzi+ 2yzj+ (X2+y²)k a. State whether F is conservative, and give a one-sentence justification for your statement b. Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation x=at, y=bt, z=ct (0sts1). c. Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(x, y, z) corresponding to F, such that F=-VU.

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1) Verify Stoke's Theorem for the vector field F(x, y, z) = 2zı + 3x) + 5yk, taking S to be the portion of the paraboloid z = 4 - x2 – y² for which z 2 0 with upward orientation, and C to be the positively oriented circle x2 + y2 = 4 that forms the boundary of S in the xy - plane. %3D Ans: 12n