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4. Suppose S is the surface z= x² + 4y? Tying beneath the plane z=1. Orient...
4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient...
4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V= <y,-X2,xz'>[12]
Suppose S is the surface z= x2 + 4y2, lying beneath the plane z=1. Orient S...
Suppose S is the surface z= x2 + 4y2, lying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V= <y, -x,x=2>[12]
Suppose S is the surface z= x2 + 4y2, lying beneath the plane z=1. Orient S...
Suppose S is the surface z= x2 + 4y2, lying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V= <Y,-X+,x=2>[12]
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>....
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisph...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
Let S be the part of the plane 2x+4y+z=4 2 x + 4 y + z = 4 which lies in the first octant, oriented upward. Use the Sto...
Let S be the part of the plane 2x+4y+z=4 2 x + 4 y + z = 4 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F=4i+4j+3k F = 4 i + 4 j + 3 k across the surface S
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)...
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate the flux integral of the vector field F 2i + j + 3k across the surface S (with N being the uni...
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate the flux integral of the vector field F 2i + j + 3k across the surface S (with N being the unit upward vector normal to the plane). B.I 48 C. I 72 E. 1 24
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate...
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
4. Consider the surface (cone) S given by (a) Calculate the surface area of S (b) Equipping S wit...
4. Consider the surface (cone) S given by (a) Calculate the surface area of S (b) Equipping S with an upwards pointing unit normal (one where the z-component of the normal vwctor is positive), calculate the flux of the vector field Fla,,) (x, y, 0) through S , y, z)
4. Consider the surface (cone) S given by (a) Calculate the surface area of S (b) Equipping S with an upwards pointing unit normal (one where the z-component of the...
4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V= <y,-X2,xz'>[12]
Suppose S is the surface z= x2 + 4y2, lying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V= <y, -x,x=2>[12]
Suppose S is the surface z= x2 + 4y2, lying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V= <Y,-X+,x=2>[12]
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
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)...
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate the flux integral of the vector field F 2i + j + 3k across the surface S (with N being the unit upward vector normal to the plane). B.I 48 C. I 72 E. 1 24
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate...
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
4. Consider the surface (cone) S given by (a) Calculate the surface area of S (b) Equipping S with an upwards pointing unit normal (one where the z-component of the normal vwctor is positive), calculate the flux of the vector field Fla,,) (x, y, 0) through S , y, z)
4. Consider the surface (cone) S given by (a) Calculate the surface area of S (b) Equipping S with an upwards pointing unit normal (one where the z-component of the...
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