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Use a parametrization to set up an integral to find the flux || F.Nds of F(x,y,z)=...
section 16.6 Use a parametrization to find the flux SSFor Fón do across the surface in...
section 16.6
Use a parametrization to find the flux SSFor Fón do across the surface in the given direction. F= - xi – yj + 3z?k outward (normal away from the z-axis) through the portion of the cone z = Vx² + y2 between the planes z = 3 and z = 4. The flux is (Type an exact answer, using a as needed.)
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...
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za. 04: Use a surface integral to find the outward flux of F = x i + y j + z k th...
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
Use the Divergence Theorem to evaluate If /F. F.NDS and find the outward flux of F...
Use the Divergence Theorem to evaluate If /F. F.NDS and find the outward flux of F through the surface of the solid S bounded by the graphs of the equations. Use a computer algebra system to verify your results. F(x, y, z) = xeļi + ye?j + ek S: z = 9 - y, z = 0, x = 0, x = 6, y = 0
(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]
Please do your best with the handwriting. Thank you very much 14. F(x. y. z)4xzi +...
Please
do your best with the handwriting. Thank you very much
14. F(x. y. z)4xzi + yj + 4xyk S: z 9 x2y'. z 20 15. F(x, y. z)i + yj + zk S:z x- y In Exercises 7-18, use the Divergence Theorem to evaluate IJ. F.NdS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results
14. F(x. y. z)4xzi...
(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) = z2k through the upper hemisphere of the sphere x2 + y2 + z2 = 4, oriented away from the origin. If necessary, enter P as rho, 8 as theta, and o as phi. B D Flux IT do de А A= B= C = D= (b) Evaluate the integral. Flux = F.dĀ= SI S
Il Evaluate the surface integral F.ds for the given vector field F and the oriented surface...
Il Evaluate the surface integral F.ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y) - zk, S consists of the paraboloid y = x2 + 22,0 Sys1, and the disk x2 + z2 s 1, y = 1. Evaluate the surface integral F.ds for the given vector field F and the oriented surface S....
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shad...
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis defined by z2 +--4for-1SS3,oriented away from y-axis. F-3 (b) Sis given by z2 + y2 + z2-9and F-1n+zk. (c) S is the conical face -V+ over the region r S 2 on the zy-plane, oriented downwards.
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
section 16.6
Use a parametrization to find the flux SSFor Fón do across the surface in the given direction. F= - xi – yj + 3z?k outward (normal away from the z-axis) through the portion of the cone z = Vx² + y2 between the planes z = 3 and z = 4. The flux is (Type an exact answer, using a as needed.)
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...
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
Use the Divergence Theorem to evaluate If /F. F.NDS and find the outward flux of F through the surface of the solid S bounded by the graphs of the equations. Use a computer algebra system to verify your results. F(x, y, z) = xeļi + ye?j + ek S: z = 9 - y, z = 0, x = 0, x = 6, y = 0
(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]
Please
do your best with the handwriting. Thank you very much
14. F(x. y. z)4xzi + yj + 4xyk S: z 9 x2y'. z 20 15. F(x, y. z)i + yj + zk S:z x- y In Exercises 7-18, use the Divergence Theorem to evaluate IJ. F.NdS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results
14. F(x. y. z)4xzi...
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z2k through the upper hemisphere of the sphere x2 + y2 + z2 = 4, oriented away from the origin. If necessary, enter P as rho, 8 as theta, and o as phi. B D Flux IT do de А A= B= C = D= (b) Evaluate the integral. Flux = F.dĀ= SI S
Il Evaluate the surface integral F.ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y) - zk, S consists of the paraboloid y = x2 + 22,0 Sys1, and the disk x2 + z2 s 1, y = 1. Evaluate the surface integral F.ds for the given vector field F and the oriented surface S....
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis defined by z2 +--4for-1SS3,oriented away from y-axis. F-3 (b) Sis given by z2 + y2 + z2-9and F-1n+zk. (c) S is the conical face -V+ over the region r S 2 on the zy-plane, oriented downwards.
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
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