4 The flux of the curl of the vector field F(x, y, z) = (xy + e¯³², xz − ze³¹², xyz), (x, y, z) € R³ through the surface S = {(x, y, z) Є R³ : (x+3)² + y² + z² = 27, x ≥ 0} oriented such that its normal vector has a positive second component, equals: (A) -27π (B) 0 (C) 18π (D) 27π

4 The flux of the curl of the vector field F(x, y, z) = (xy + e¯³², xz − ze³¹², xyz), (x, y, z) € R³ through the surface S = {(x, y, z) Є R³ : (x+3)² + y² + z² = 27, x ≥ 0} oriented such that its normal vector has a positive second component, equals: (A) -27π (B) 0 (C) 18π (D) 27π

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

2. For the vector field F (x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div (F)div (F) (b) curl (F)curl(F) (c) div (curl (F))
= Calculate the flux of the vector field F(x, y, z) = (5x + 9)ỉ through a disk of radius 3 centered at the origin in the yz-plane, oriented in the negative x-direction. Flux =
f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?
Compute the flux of the vector field F(x, y, z) = 3ỉ + 23 + 2k through the rectangular region with corners at (1, 0, 0), (1, 1, 0), (1, 1, 2), and (1, 0, 2) oriented in the positive x- direction, as shown in the figure. Flux = 0 (Drag to rotate)
please help!
Suppose the vector field v(x, y, z) = (4xy², -4xz², 5x) represents the velocity field of a fluid. Find the circulation where C is the intersection of paraboloid z = 4 - 2x² - 2y2 with cylinder x² + y² = 4. Enter an exact answer. Provide your answer below: Sev-dr = [v. v. dr,
Compute the flux of the vector field = yi + 53 − xzk through the surface S, which is the surface y = x² + z², with x² + z² ≤ 1, oriented in the positive y-direction. flux =
Compute the flux of the vector field F = 3yi + 4j – 3xzk through the surface S, which is the surface y = x2 + z2, with x2 + z2 < 1, oriented in the positive y-direction. flux =
Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve thatconsists of two line segments C1 and C2, where C1 has vertices (−1, 0) and (0, 1)and C2 has vertices (0, 1) and (1, 0). C is oriented clockwise.(a) Sketch C accurately.(b) Find the work done by F by moving a particle along the path C in the givendirection.
Let + y³)%¸ æyz 7 4 F = x² + be a vector field on U = {(x, y, z) E R° | (x, y) + (0, 0)}. Find its curl and divergence. V × F = V · F =
Find the flux of the vector fieldF(x, y, z) =(x)i+(y)j+(z)kthrough the surface S of the paraboloid z=x^2 + y^2, for 0 ≤ z ≤ 9,where the unit normal n to S has a negative k component. (This the flux through the side of the paraboloid.)