Use a parameterization to find the flux F•n do of F = z'i+ xj - 2zk in the outward direction (normal away from the x-axis) across the surface cut from the parabolic cylinder z = 9- y? by the planes x = 0, x = 1, and z= 0. ..... The flux is

Q: Use a parameterization to find the flux F•n do of F = z°i+ xj – 4zk in the outward direction (normal…

A: We have to find the flux ∬SF·ndσ of F=z2i+xj-4zk in the outward direction across the surface cut…

Q: Use the surface integral in Stokes Theorem to calculate the flux of the curl of the field F = 5zi +…

A: Stoke' s theorem ∫CF.dr =∫∫scurl F .ds Given  F=5z , x , 2y  and r =r cosθ , r sinθ , 25-r2   ;…

Q: 1. Determine the velocity field v so that the surface F(r, y, t) (y+t)+ (r +t)2 - a 0 to be a…

A: Solution:

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = (5x3…

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Q: use a parametrization to find the flux f f s F . n dsacross the surface in the specified direction.…

A: Consider the function: Given   F=4xi+4yj+2kSurface cut from the bottom of the paraboloid z=x2+y2 by…

Q: Use Stokes' Theorem to find the line integral | (17 + 2y°)i + (w + =°)5 +(= + 2r*)k) • dř where C is…

A: Stokes' Theorem: Let S be a oriented smooth surface which is bounded by the curve C (simple closed,…

Q: Consider the curve C between the points (1,0, 1) and (0, 1, 1) at the intersection of the cylinder…

A: To evaluate the line integral along with the curve c of ω=−ydx+xdy+dz.

Q: Use a parametrization to find the flux I F.n do across the surface in the given direction. F= - xi -…

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Q: Let f(x, y, z) = (2x + 4z + 10)/xy + 2. %3D a. Evaluate the line integral of f along the line…

A: We will find out the required solution.

Q: Q3: A- Use Greens theorem to evaluate the circulation or flux for the velocity field S(x, y) =- x+y…

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Q: Find the circulation and flux of the field F = - xi – yj around and across the closed semicircular…

A: The circulation of a vector F=M i+ N j along the curve C is defined by ∮CF·T ds=∮CMdx+Ndy. Here…

Q: Use a parameterization to find the flux F•n do of F = zʻi+ xj - 2zk in the outward direction (normal…

A: Given : A Parabolic cylinder z = 1 - y² by the planes x = 0, x = 1, and z = 0

Q: Use Stokes' theorem to evaluate frotF. ds. F(x, y, z) = xyi + e²j + xy²k; S consists of the four…

A: To find- Use Stokes' theorem to evaluate ∫SrotF·dS, Fx, y, z = xyi + e2j + xy2k; S consists of the…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

A: The given question can be solved as shown in step2

Q: Let F(x, y, z) = z tan-1(y?)i + z In(x2 + 8)j + zk. Find the flux of F across S, the part of the…

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Q: 1. Determine the velocity field v so that the surface F(r, y.t) = (y+t)+ (z+t)? - a² = 0 to be a…

A: The given surface is - F(x,y,t) = (y+t)2 + (x+t)2-a2.......(1) The velocity field (V→) components…

Q: Use a parameterization to find the flux SSF. S plane x+y+z=5a that lies above the square 0≤x≤a,…

A: We have to find the flux

Q: Let v (2, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the surface…

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Q: Let f(x, y, z) = (2x + 4z + 10)/xy + 2. %3D a. Evaluate the line integral of f along the line…

A: We will evaluate the given integral.

Q: Evaluate the flux integral F-ds where Pis the part of the paraboloid -= 4-x -y above the xy plane…

A: Any integral which is to be evaluated at the surface is called the surface integral. Divergence…

Q: Find the flux of the following vector field across the given surface with the specified orientation.…

A: Let r be the vector on the surface of  the cylinder y=6x2 for 0 ≤ x ≤ 4​, 0 ≤ z ≤ 2​.Let's…

Q: Find the flow of the velocity field F = (y + z)i + xj - yk, where velocity is measured in meters per…

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Q: Let F(x, y, z) = z tan-1(y2)i + z³ In(x² + 6)j + zk. Find the flux of F across S, the part of the…

A: Using divergence theorem:  ∬SF.dS=∭VdivF.dV…

Q: use a parametrization to find the flux f f s F . n dsacross the surface in the specified direction.…

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Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Use a parametrization to find the flux F•n do across the surface in the given direction. F= - xi -…

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Q: Use a parameterization to find the flux do of F = z²i+ xj – 4zk in the outward direction (normal…

A: Apply Divergence theorem to the given surface integral, ∬F.ndσ=∫∫∫DivFdV

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= zi+…

A: Calculate the flux of the curl of the field F = z i + 5 x j + y k, by using the surface integral in…

Q: Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the…

A: Given surface 'S' is surrounding region D bounded by the planes y=0, z=0, z=2-y and z=1-x2

Q: Use a parameterization to find the flux F•n do of F = z'i+xj- 4zk in the outward direction (normal…

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Q: Let v = (5, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the…

A: Given, v→=5,y sinz, cosz Flux=∫∫Sv⇀.ds we have divergence theorem, ∫∫Sv⇀.ds=∫∫∫Sdiv v⇀.dv div…

Q: Let E be the solid region bounded by the upper half-sphere x2 + y² + z² = 4 and the plane z = 0. Use…

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Q: 5. Find the flux of F (x,y,z) = y cos(z)i-yx sin(x) j+ xy³k through the outward oriented cube of…

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Q: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

A: Given F=2i+2j+2k,radius=5 and x+y+z=1 plane

Q: Let E be the solid region bounded by the upper half-sphere x² + y? + z2 = 4 and the plane z = 0. Use…

A: Flux of a vector field F→ along surface S =∫∫SF→.dS Divergence theorem  ∫∫SF→.dS→=∫∫∫E divF→dV Where…

Q: Use a parameterization to find the flux F•n do of F = z'i+xj-3zk in the outward direction (normal…

A: We have to fin the flux ∬SF⋅ndσ, where F=z2i+xj−3zk. The intersection of the parabolic cylinder…

Q: The field F = -y³i + (x³ + e=y)j + 0k is the velocity field of a flow in space. Determine the…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = (-5x + 2y) i + (6x…

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Q: Confirm that the force field F(c, y) = 2xy³i + 3x?y?j is conservative in some open connected region…

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Q: Let w = e dr + 6x dy + sin(r) dz be a one-form on R*. Find the line integral of w going…

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Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Given surface, F=2xyi+2yzj2xzk           ...(1) Given plane, x+y+z=2a                ...(2) Where…

Q: Find the flux of F = (3z + 1)k upward across the hemisphere x2 + y2 + z2 = a2, z>= 0 (a) with the…

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Q: Use Gauss' Divergent Theorem to calculate F. dS where F = (2x + sen (et1)) i+3y²j+ cos(z²)k and S is…

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Q: find the surface integral of the field F over the portion of the given surface in the specified…

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Q: Let S be the cylinder x² + y² =a²2, 0≤zsh, together with its top, x² + y² sa², z = h. Let F = -7yi +…

A: Given : Surface S is the cylinder x2+y2=a2, 0≤z≤h, together with its top, x2+y2≤a2, z=h and  F→=-7y…

Q: find the outward flux of F across the boundary of D. F = xz i + yz j + k D: The entire surface of…

A: Consider the given vector field. F = xz i + yz j + k

Q: See attached photo.  Please provide the flux.

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Q: find the outward flux of F across the boundary of D. F = (6x + y)i - (x + z)j + 4yz k D: The region…

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Q: Find an equation for the plane through the origin such that the circulation of the flow field F = zi…

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =xi+ 5xj +zk…

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