Use the Divergence Theorem to evaluate F. dS where S is the sphere r² + y² + z² = 9 and F = (3r, 2y, 0). (Hint: the volume of a sphere is V = 4r³/3.)

Q: Use the divergence theorem to evaluate F.dS, where F = and S is the surface bounded by x2+y²=4, z…

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Q: Verify the formula [[F.nds = [ div F dV in the Divergence Theorem by evaluating the surface integral…

A: The function given is as follows: Fx, y, z=2xi^-yzj^+z2k^ With σ being the paraboloid z=x2+y2 capped…

Q: For the vector A = ar r2 + az 2z, satisfy the divergence theorem in the circular cylindrical region…

A: Consider the given vector: A→=arr2+az2z and a circular cylindrical region surrounded by  r=5,z=0,…

Q: Using the Divergence Theorem, evaluate I= F dS where S is the sphere of radius 2 centered at the…

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Q: For the vector A = ar r2 + az 2z r = 5, z = 0 and z = 4 in the circular cylindrical region…

A: The objective is to prove the divergence theorem for the vector function A=arr2+az2z for the…

Q: For F = xy?a, + yz²a, – x²za,, use divergence theorem to evaluate ff, F. dS where S is the sphere of…

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Q: Let E be the region bounded by the hemisphere x² + y? + (z – 2)² = 4, 2 < z < 4, and the plane %3D z…

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Q: Use the Divergent Theorem to find the outward flux ofF = yi+3yj+ 322k across to the boundary of the…

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Q: Use the Divergence Theorem to calculate F.dS, where F (x, y, 2) = x² yzi + 2yzj – xyzk and %3D S is…

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Q: Use the Divergence Theorem to evaluate F. ds, where F(x, y, z) = z?xi + (+ tan zj + (x²z + y2)k and…

A: We are given a closed surface integral and we have to use the Divergence Theorem to evaluate that.

Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: * Use the Divergence theorem to find , F. dS where F(z, y, z) = (zy, y, -zy) and S is closed surface…

A: Using surface integral, answer is 8π

Q: use the divergence theorem to compute: F(x,y,z)=x2i+y2j+z2k; for the boundary of the solid region…

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Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Let F= [x, y, z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Given : F = x,y,z

Q: Verify the divergence theorem, ffaw F · dS = S[fw, Div FdV, for F(x, y, z) = (z)i + (y)j + (x)k,…

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Q: Let S be the portion of the paraboloid z = r² + y? below z = 4 together with the disk a2 + y² < 4 in…

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

A: See the details solution in below

Q: Use divergence theorem to evaluate F •dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

A: According to the divergence theorem ∬SF¯·ds¯=∫V∇·F¯dV, where V is the volume bounded by the closed…

Q: Use the divergence theorem to compute the value of flux integral F. dS, where F(x, y, z) = 5yj - 5zk…

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Q: Verify Gauss Divergence Theorem for F = (x3- yz)i+ (y² - xz)j+ (z3 – xy)k %3D taken over a…

A: GivenF→=x3-yzi^+y2-xzj^+z3-xyk^taken over a rectangular  parallelepiped bounded by 0≤x≤a,0≤y≤b and…

Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r+y + z…

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Q: Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of…

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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: Verify the divergence theorem for F=3i + xy j + x k  taken over the region bounded by z = 4 - y^2 ,…

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Q: Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F…

A: We must apply the Divergence theorem on a closed solid, but the surface S is not closed (it is just…

Q: Use divergence theorem to evaluate F·dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

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Q: b) Use the divergence theorem to compute ff, F ñ ds, where S is bounded by x+ y + 2z = 2 located in…

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Q: Verify the Divergence Theorem by evaluating [[F. F. N ds as a surface integral and as a triple…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = (6x2…

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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: Verify the Divergence Theorem SI div F av F. dS S E for F(r,y,2) = z i+ yj+xk and where E is the…

A: Given that Fx,y,z=z i+ y j +x k and E is the solid ball x2+y2+z2≤16. First find the divergence of F.…

Q: ` Use the Divergence Theorem to calculate the surface integral F-dS, where F = (2x, 3y, 0 S and S is…

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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: Apply the divergence Theorem for the vector function Ả = xỉ + yj + zk, the boundary surface between…

A: Here we will find out the required value.

Q: The flux of F(x, y, z) = 2³î – r³}+ y®k, where o is the sphere | x2 + y? + z2 = a² with outward…

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Q: Use the Divergence Theorem to evaluate the surface integral |a? – 3y + 62) ds, S. here S is the…

A: Given the surface integral ∬Sx2-3y+6zdS, where S is the sphere x2+y2+z2=9. The integrand is a scalar…

Q: Use the divergence theorem to evaluate F.dS, where F (x, y, z) = zxi – e"´j+ 4zk and S is the…

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Q: Let F(x, y, z) = 2z? xi + (y + tan(z))j + (2x²z – 2y²)k. Use the Divergence Theorem to evaluate F.…

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Q: use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the…

A: By divergence theorem

Q: b) Use the divergence theorem to compute ff, F · i ds, where S is bounded by x +y + 2z = 2 located…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2 i…

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Q: Given F = ryx – ỳ + zà, use the divergence theorem to evaluate f, F. dS over the closed surface…

A: Given F→=xyx^-12y2y^+zz^The closed surface consisting of the three surfacesfz=z-4+3x2+3y2when…

Q: Use the Divergence Theorem to find the flux of F accross S; that is calculate LlF• nds where F(x, y,…

A: Topic : vector calculus

Q: Use the Divergence Theorem to evaluate  F · dS,  where  F(x, y, z) = z2xi +  + ((1/3)y3 + cos z)j +…

A: Given data:

Q: Use the Divergence Theorem to find F- ndS, where F = (y°z,x²z,z') and the surface S is the sphere x…

A: See the details solution below

Q: use the Divergence Theorem to find the outwardflux of F across the boundary of the region D. F = (x…

A: To Determine: use the Divergence Theorem to find the outward flux of F across the boundary of the…

Q: Let F(x, y, 2) = 32?ai+ (y³ + tan(z))j+ (3x²z- 4y?)k. Use the Divergence Theorem to evaluate fs F dS…

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