9. Use Stokes' Theorem to evaluateF. drwhere F(r, y, 2) = (2 – y) i+ (x + 2)j – (x+ y) k and C is the intersection of the paraboloid z = 2 – 2? – y² and theplane z = 1 with a counterclockwise orientation looking down the positive z-axis.

The given problem is to evalute the contour integral using stokes theorem, where surface C is the…

Answered: 9. Use Stokes' Theorem to evaluate F.…

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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AM (2) - Edited Let W be the plane with equation x + 2y + 2z = 1. Define the function f (x,y, z) to be f(x, y, z) = distance from (x, y, z) to W. %3D (a) For each real number k > 0, the level surface f(x, Y, z) = k can be described in terms of other familiar surfaces. Give a geometric description of the level surface f(x, y, z) = k. Be as precise as possible when explaining your answer. %3D (b) For each real number k > 0, produce an explicit equation for the level surface f(r, y, z) = k. (c) Consider the function g = f² (distance square). Find the partial derivatives (r, y, z) and Buể (T, y, z). What do you notice? (d) Let F(t) be a single-variable function. The following table gives some relevant values of this function. F F' F" t = 0 -4 10 t = 1 13 -1 t = 2 -2 9. -3 82h aydz Suppose that h(x, y, z) = F(g(x, Y, z)). Find values of (0,0, 2) and (0, 0, 2) 3:07 7 days ago Dreamland Glass Animals 3:21 Dreamland Glass Animals The Score (Expanded Editi Fugees ADE 7 days ago 3:59 Heat Waves…
Use Stokes' Theorem to evaluate F. dr, where C −8y³i+8x³j+7z³k and C is the intersection of F 2 the cylinder x² + y² = 1 and the plane 2x + 3y + z = 6 (oriented counterclockwise as seen from above). = [F-&x=0 F. dr C
The part of the plane with vector equation r(u, v) = (u + v, 2 – 3u, 1 + u – v) that is given by 0 su< 2, –1 < v< 1
Find an equation of the tangent plane to the given parametric surface at the specified point. r(u, v)=u²i+ 3us invj +ucos vk; u=2,v=0 a. 24(z+2)-6(x-4)=0 b. 24(2-2) + 6(x+4)=0 24(z-2)-6(x-4)=0 C. d. 24(z-2) + 6(x-4)=0 12(z+2)-6(x-4)=0 e.

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9. Use Stokes' Theorem to evaluate F. dr where F(z, y, 2) = (2 – y) i + (x + 2)j – (x + y) k and C is the intersection of the paraboloid z = 2 – a – y² and the plane z = 1 with a counterclockwise orientation looking down the positive z-axis.