Calculate the flux of F across G. F(x, y, z) = 2xi + 2yj + 2zk; G is the surface of the sphere x2 + y2 + z2 = 4 in the first octant %3D

Q: Let F(x, y, z) = z tan-(y²)i + z³ In(x² + 2)j + zk. Find the flux of F across S, the part of the…

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Q: find the outward flux of F across the boundary of D. F =-2x i - 3y j + z k D: The upper region cut…

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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: 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: 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: use the Divergence Theorem to find the outward flux of F across the boundary of the region D. F = y…

A: The divergence theorem states:

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

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Q: Let F (x, y, z) = and G be the solid | Let below the paraboloid % = 4 – x* – Y° and above the…

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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: Let S be the cylinder x +y = a°, 0szsh, together with its top, x² +y° sa, z=h. Let F= - 4yi + 4xj +…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z)=z³ i-x³j+y³ k across the sphere x² + y² +…

A: This is a problem of vector calculus.

Q: Find the outward flux of F through S. F-Ñ dS where F(z, y, z) = -3zî+y³j+yk, and S is the surface of…

A: The general form of a vector valued function in three dimensions is given by F→=F1i^+F2j^+F3k^,…

Q: Use the Divergence Theorem to evaluate F.N ds and find the outward flux of F through the surface of…

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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: Use the Divergence Theorem to evaluate F.NO N ds and find the outward flux of F through the surface…

A: Note the following result :  Gauss divergence theorem : ∫∫SF⇀.N⇀dS =∫∫∫Ddiv(F⇀)dV ,where S is an…

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 F(x, y, z) = z tan-¹(y²)i + z³ In(x² + 3)j + zk. Find the flux of F across S, the part of the…

A: The given problem is to find the flux of vector field over the given surface of part of the…

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…

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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: 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: Find the flux of F = z²k upward through the part of the sphere æ² + y² + z² = a² in the first octant…

A: Given vector field is  F=z2k to find the flux through sphere x2+y2+z2=a2 in the first octant.

Q: Let F(x, y, z) = z tan-(y?)i + z³ In(x? + 4)j + zk. Find the flux of F across S, the part of the…

A: The given vector field is. Fx,y,z=z tan-1y2i^+z3 lnx2+4j^ +zk^ Let S be the top of the paraboloid…

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: Use the Divergence Theorem to calculate the flux of F across S, where F = zi + yj + zxk and S is the…

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Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 4)j + zk. Find the flux of F across S, the part of the…

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Q: Let F (x, y, z) = and G be the solid %3D | below the paraboloid % = 4 – x" – y° and above the…

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Q: Use the Divergence Theorem to calculate the outward flux of F = (r3 + y, y + z3, z3 + 23) across S:…

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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 outward flux of F across the boundary of the region D. F=x*i-…

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

A: Divergence Theorem states that  Where S is a closed surface, and E is the region inside that…

Q: Let F(x, y, z) = z tan−1(y2) i + z3 ln(x2 + 8) j + z k. Find the flux of F across S, the part of the…

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Q: 7. Find the flux of F(z,y, 2) = ri+yj+zk through the portion of the paraboloid z = 1+z²+y° that is…

A: Given

Q: Let S be the piece of the surface z = 9– x2 that lies inside the cylinder x2 +y? = 9, and let F =…

A: According to question, Given Surface, z = 9 -x2 ,This surface lies Inside the cylinder x2 + y2 = 9,F…

Q: oriented

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Q: Let F(x, y, z) = z tan-(y2)i + z³ In(x2 + 9)j + zk. Find the flux of F across S, the part of the…

A: Get points of intersection of the paraboloid and z=3:  Thus, point of intersection is a circle in…

Q: Use the Divergence Theorem to calculate the Flux of F(x,y, z) = 1xi+ 5yj+ 2zk, E is the surface of…

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Q: Find the flux of F = (y +xz)i + (y + yz)j – (2x + z²)k upward through the first octant part of the…

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Q: Find the flux of F(x,y,z) = (-x,-y, z³) , across S. Where S is the part of the cone z = /x² + y²…

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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)= (sin (zy))i +(z° cosh x)j+(z² )k. Find the flux of F across the positively oriented…

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Q: QA-evaluate the flux of the filed F-xi+yj+zk through the upper part of the cylinder x² + z² = 1 that…

A: Given

Q: Let S be the piece of the surface z = 9-r that lies inside the cylinder r2 +y² = 9, and let F = (x,…

A: Given, S be the piece of the surface z=9-x2 that lies inside the cylinder x2+y2=9, and let F=x,y2,z.…

Q: Use the Divergence Theorem to evaluate N ds and find the outward flux of F through the surface of…

A: We have to find the flux

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: The region W lies between the spheres a? + y? + z2 = 9 and æ? + y² + z² = 16 and within the cone z =…

A: Here we can use divergence theorem to find the flux of the vector valued function. Divergence…

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: 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…