Compute the flux of F (x, y, z) = (y, z, x) across the surface S : R(u, v) = (u+2v, v – u, u), where u e [-1, 1] and v E [0,2].

Q: 6. Find the flux of F (x,y, z) = y cos(z) i – y x sin(x)j+xy³k through the outward oriented cube of…

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Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 4 + x + 2y above…

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Q: Find the flux of F(x, y, z) = 4а, 32 + 2?, across the positively oriented surface 2 S given by R(u,…

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Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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Q: Let  F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 3)j + zk.  Find the flux of F across S, the part of the…

A: The flux of any vector field F→(x,y,z) across some closed surface S, such that the surface S bounds…

Q: Find the flux of F(x,y,z) = sin(xyz) i+ xy j + ze*/5 k across the part of the cylinder y? + 2 z? = 4…

A: According to question,Fx,y,z= sin xyzi +xy j + z ex5 k,equation of cylinder,y2 + 2z2 =4planes, x = 1…

Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

Q: Let S be the cylinder x +y a, 0szsh, together with its top, x +y sa, z=h. Let F= -7yi + 7xj + 7x k.…

A: Given data: S is the cylinder, with its top x2+y2≤a and height0≤z≤h. Also Given a vector F→ Such…

Q: Find the flux of the field F(x, y, z) = z2 i + x j - 3 z k outward through the surface cut from the…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x² + y)i+z°j+ (e° – z)k across the…

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Q: Find the flux of the vector field F (x, y, z) = (e-y, -y, x sin z) across the positively oriented…

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Q: 2. The task is to determine the flux of B across G, where G is the positively-oriented portion of…

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Q: Let = (xz, 2 4xyz, rz) be the velocity field of a fluid. Compute the flux of i across the surface…

A: Flux of velocity about a surface is the measure of amount of velocity of fluid hitting the surface.…

Q: Compute the flux of the vector field F(x, y, z) = 2xj+ 4yk through the surface S, where S is the…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x – z)i + (y – x)j+ (z – y)k %3D -…

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Q: Find the net flux of the vector field F(x, y, z) = (2x, - 2y, z) over the closed surface enclosed by…

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Q: Use the divergence theorem to find the flux of F = [x²yz, -xy² z, 6 – 5z2| on the hemisphere S =…

A: Consider the given function. The divergence theorem is defined as. Now, find the value of div F.

Q: Find the net outward flux of F = a x r across any smoothclosed surface in ℝ3, where a is a constant…

A: Net outward flux is ∇.F ∇=i∂∂x+j∂∂y+k∂∂za=a1i+a2j+a3kr=xi+yj+zk

Q: Find the flux of F through the surface S. F(x, y, z) = xi + yj + xzk S is the cone r(u, v) = ⟨u…

A: flux related problem.....

Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

Q: 3. Calculate the rotational flow of F(x, y, z) = -j + xj + x²k, that goes through the cone given by…

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Q: Let F(x, y, z) = (2x, y, –2z) be the velocity field of a fluid. (b) Let o be the boundary of the…

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Q: Compute the upward flux of F across the surface defined by R(u,v) = where 0 ≤ u ≤ 2 and 0 ≤ v ≤ 1.

A: The given surface is Ru, v=<2u, 3v, u2-v2>.......(i), where 0≤u≤2 and 0≤v≤1 and F→x, y,…

Q: Find the flux of the vector field F(x, y, 2) = yj + k where o is the portion of the cone =' = 4(x² +…

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Q: Evaluate the outward flux of the vector field F = (2x² – 5e" + sin(z²), –4ry + In(x*), 5z – 3x²y®)…

A: We can see that the region given here is closed, so…

Q: Use the divergence theorem to evaluate the flux of F(x, y, z) = 2xyi+ yzj+ z? k across the surface…

A: We will use Divergence theorem to evaluate the flux.

Q: Let v = (a*z, 2 – 2xyz – 3y + x*y, 3z – x*z) be the velocity field of a fluid. Compute the flux of v…

A: Given the vector field         v=x2z,2-2xyz-3y+x2y,3z-x2z

Q: Let F(x, y, z)=(y)i +(x)j+(z³)k. Find the flux of F the positively oriented across closed surface S…

A: Here  ∇·F→ = 2x + 2y + 2z = 2(x+y+z) R.H.S = ∫∫∫V ∇·F→.dv R.H.S =…

Q: Compute the net outward flux across the sphere r²+y²+z (r*, y², 2ª).

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x°i+ 3.x²yj+ 33xyk across the surface…

A: According to the given information, it is required to use the divergence theorem to find the flux.

Q: Find the flux of the vector field F = (y, – z, x) across the 2 + 4x + 3y above the rectangle part of…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the outward flux of F= (x')i+(y²)}+(z²)k across the boundary of the region D, where D is the…

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Q: Compute the flux of the vector field F(x, y, z) = 3x + 3yk through the surface S, where S is the…

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Q: Let  F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 10)j + zk.  Find the flux of F across S, the part of…

A: let, F(x,y,z)=ztan−1(y2)i+z3ln(x2+10)j+zk Find the flux of F across the part of the…

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x³i + 3x²yj + 24xyk across the surface…

A: Flux of a vector field over a closed surface is equal to the divergence of the field in the volume…

Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 3+ 4x + 2y above

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Q: Find the total flux of the field x+ /1+ y² + z² 2y + V1+x²+ z² \3z + /1+x² + y², F(x,y, z) = out of…

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Q: Find the flux of the vector field F(x,y,z) = xi – yj + zk across o, where o is the portion of the…

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Q: 3) Use the Divergence Theorem (Gauss's Theorem) to calculate the flux of F = (x - y)i + (y-z)j +…

A: Here we have to use Divergence theorem to calculate the flux.

Q: Use divergence theorem to find the flux of F(x, y, z) = x² yì – xy² j+ (z+ 2) k ; o is the surface…

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Q: Let - (xz, 5 - 4xyz, xz) be the velocity field of a fluid. Compute the flux of i across the surface…

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Q: Let F(x, y) = (2x + y³, 2y – x4). Compute the flux oF. F.n ds of F across the circle of radius 5…

A: Given function can be written as, Region bounded by the circle of equation,

Q: 8. Use the Divergence Theorem to find the outward flux of F(r, y, 2) = (y² + 2) i+y²j+(e® + z) k…

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

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Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

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Q: Find the work done by the force field F(x, y, z) = (x – y², y – z², z – x2) on a particle that moves…

A: We have to find the work done by the force field F(x,y,z)=&lt;x-y2, y-z2, z-x2&gt; on a particle…

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: Given that    Fx,y,z=z tan-1y2i+z3Inx2+6j+2k Also, the part of paraboloid x2+y2+z=6 that lies above…