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(1 point) Compute the flux of the vector field F(x, y, z) = 3 + 2+...
(1 point) Determine whether the flux of the vector field F through each surface is positive, nega...
(1 point) Determine whether the flux of the vector field F through each surface is positive, negative, or zero. In each case, the orientation of the surface is indicated by the gray normal vector. Enable Java to Enable Java to [Enable Java to make this image make this image make this image interactive] interactive] interactive Choose Choose Choose Enable Java to [Enable Java to make this image make this image interactive] interactive] Choose Choose
(1 point) Determine whether the flux...
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them....
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them.) Enable Java to make this image Enable Java to make this image interactive] Enable Java to make this image Enable Java to make this image Enable Java to make this image Enable Java to make this image interactive] 1 point...
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them....
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them.) Enable Java to make this image Enable Java to make this image interactive] Enable Java to make this image Enable Java to make this image Enable Java to make this image Enable Java to make this image interactive]
1 point)...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
compute the flux of the vector field F(x,y,z) = x^2yi -2yzj + x^3y^2k over the surface...
compute the flux of the vector field F(x,y,z) = x^2yi -2yzj + x^3y^2k over the surface of the surface of the unit cube S : 0≤x≤1, 0≤y≤1 , 0≤z≤1 verify answer using Gauss divergence therom
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the r...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
(a) Set up a double integral for calculating the flux of the vector field F(x, y,...
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = (x2, yz, zº) through the open-ended circular cylinder of radius 5 and height 4 with its base on the xy-plane and centered about the positive z-axis, oriented away from the z-axis. If necessary, enter 6 as theta. Flux = -MIT" dz de A= BE C= D= (b) Evaluate the integral. Flux = S]
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
(10) Consider the vector field F (x, y, z) = (x,y, z). Clearly sketch and label three oriented surfaces S, So and S who...
(10) Consider the vector field F (x, y, z) = (x,y, z). Clearly sketch and label three oriented surfaces S, So and S whose flux is negative, zero, and positive, respectively. Be sure to indicate orientations. Explain your conclusions
(10) Consider the vector field F (x, y, z) = (x,y, z). Clearly sketch and label three oriented surfaces S, So and S whose flux is negative, zero, and positive, respectively. Be sure to indicate orientations. Explain your conclusions
Question 10 Compute the flux of the vector fields F(x, y, z) =< x, y2,1 >...
Question 10 Compute the flux of the vector fields F(x, y, z) =< x, y2,1 > across the portion of the plane r+y+z=1 on the first octant, with orientation pointing toward the positive x direction. (Do not use Stokes' theorem)
(1 point) Determine whether the flux of the vector field F through each surface is positive, negative, or zero. In each case, the orientation of the surface is indicated by the gray normal vector. Enable Java to Enable Java to [Enable Java to make this image make this image make this image interactive] interactive] interactive Choose Choose Choose Enable Java to [Enable Java to make this image make this image interactive] interactive] Choose Choose
(1 point) Determine whether the flux...
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them.) Enable Java to make this image Enable Java to make this image interactive] Enable Java to make this image Enable Java to make this image Enable Java to make this image Enable Java to make this image interactive] 1 point...
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them.) Enable Java to make this image Enable Java to make this image interactive] Enable Java to make this image Enable Java to make this image Enable Java to make this image Enable Java to make this image interactive]
1 point)...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = (x2, yz, zº) through the open-ended circular cylinder of radius 5 and height 4 with its base on the xy-plane and centered about the positive z-axis, oriented away from the z-axis. If necessary, enter 6 as theta. Flux = -MIT" dz de A= BE C= D= (b) Evaluate the integral. Flux = S]
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
(10) Consider the vector field F (x, y, z) = (x,y, z). Clearly sketch and label three oriented surfaces S, So and S whose flux is negative, zero, and positive, respectively. Be sure to indicate orientations. Explain your conclusions
(10) Consider the vector field F (x, y, z) = (x,y, z). Clearly sketch and label three oriented surfaces S, So and S whose flux is negative, zero, and positive, respectively. Be sure to indicate orientations. Explain your conclusions
Question 10 Compute the flux of the vector fields F(x, y, z) =< x, y2,1 > across the portion of the plane r+y+z=1 on the first octant, with orientation pointing toward the positive x direction. (Do not use Stokes' theorem)
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