Use the Divergence theorem to evaluate F. · dS where F (x, y, z) = (4x – z²) i+ (x+3z)j+(6 – z) k and S is the surface of the solid bounded by the cylinder x? + y² = 36 and the planes z = -2 and z = 3. Note that all the three of the surfaces of this solid are included in S. is the portion of y = 11 – 3x² – 3z² in front of y = 5 with orientation in the positive y-axis direction.

Q: Let B be the region in space bounded by the planes z = 0 and z = 3x, and the cylinder x? + y² = 4.…

A: To compute the below surface integral using the Divergence theorem. Here the function is defined as…

Q: |Use the Divergence Theorem to evaluate || F•ndS where F(x, y,z)=(x+cos z)i+(2y+sin z)j+(z+e*)k .n…

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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: (6) Use the Divergence Theorem to evaluate dS, where F(x, y, 2) = xyi + (y² + e*=*)j + sin(xy)k and…

A: Given,         and

Q: Use divergence theorem to find the flux of F(x, y, z)=x²yî - xy²)+(2+2); o is the surface of the…

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

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: 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: sing the Divergence Theorem, find the outward flux of F = 2xy 21 + 2x 2yj+ 5xy k across the boundary…

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Q: Let E be the solid bounded by the xy-plane and paraboloid z = 4 - x2 - y2 so that S is the surface…

A: According to question, Paraboloid z =4-x2-y2,Fx, y, z = xz sinyz + x3 i + cosyz j + 3zy2-ex2 +y2 k

Q: 5. Use the Divergence Theorem to evaluate [[F•d$ where F = yx² i +(xy² - 3=*)j+(x² + y² )k and S is…

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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: Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple…

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Q: Use the Divergence Theorem to evaluate ff F-n do where S F(x, y, z)=(x² +cos yz, y-e², z² + x²) and…

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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: Using The Divergence Theorem, evaluate F. dS where F = -xyi+ (z – 1)j + 2³k and S is the surface of…

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

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Q: Verify the divergence theorem for F = 3 i + xy j + x k taken over the region bounded by z = 4 −…

A: According to the given information, it is required to verify the divergence theorem for,

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: Let F = (y, x, z) and S be the surface of x2 + y2 0, y 2 0,0sz< 4. Then using the divergence…

A: Using divergence theorem, ∫∫SF→·n→dA=∫∫∫∇·FdV where ∇·F denotes the divergence of F here,  F=y, x, z…

Q: Let Q be the solid region x2 + y? + z2 = 16. F(x, y) = xỉ + 4yj+ 2z k . Use the Divergence Theorem…

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Q: 4. Use divergence theorem to find the flux of F(x, y, z) = x² yî – xy²ĵ+(z+2)k; o is the surface of…

A: Consider the given vector field, F→x,y,z=x2yi^-xy2j^+z+2k^ bounded above by the plain z=2y and below…

Q: 3. Use the Divergence Theorem to evaluate F.dS where F = -zyi+(z – 1) j +k and S is the surface of…

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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: 1. Use the Divergence Theorem to evaluate /| F.dš where F.dSv F = yx? i+ (xy? - 324) j+ (x³ + y?) k…

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Q: Use the divergence theorem to evaluate ∬S F⋅N dS for F=xyzj, where S is the cylinder x^2+y^2=9, 0≤ z…

A: Use the divergence theorem to evaluate:∫∫SF→·n→dS for F→=xyzj^,where S is the cylinderx2+y2=9,0≤z≤5…

Q: Let T be the solid region in the first octant bounded by the circular cylinder Sq:z = v25 – x2 and…

A: Consider the given information.

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: 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: Let T be the solid region in the first octant bounded by the circular cylinder Sq: z = v25 – x2 Use…

A: Divergence theorem: ∭V ∇.FdV = ∬S F.n^dΣ                         (1) Given, F→x,y,z = 5+2yzi^ +…

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: Verify the divergence theorem for F = 3 i+ xy j + x k taken over the region bounded by z = 4 − y2, x…

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Q: (3) Verify the divergence theorem where (a) F(x, y, z) planes x = 0, x = 1, y = 0, y = 1, z = (b)…

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Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F =…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = 2xz i…

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Q: 4. Use the Divergence Theorem to evaluate F.dš where F = (4z – 2²) i + (z +3:) j+ (6 – 2) kand S is…

A: Solution is given below..

Q: Use the Divergence Theorem to evaluate |F.n do where F(x,y,z)=(x² +cos yz, y – e" ,z² +x*) and S is…

A: According to question given :F(x,y,z)=x2+cos yz, y-ez, z2+x2S is the boundary of the solidBounded by…

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: Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS , where…

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Q: 5. Use the Divergence Theorem to calculate the surface integral Sfs F dS: (a) F = xze'i + xz?y³j –…

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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: 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: Use the Divergence Theorem to evaluate where F = (xy + z)i+ (zy)i+ (x+z)k and the surface consist of…

A: The function given is F→=xy+zi^+13xy3j^+x+zk^. The closed surfaces are as follows: z=4-3x2-3y2,…

Q: 5. Use the Divergence Theorem to calculate the surface integral Ss F dS, where F(r, y, 2) = r'i+…

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Q: Use the Divergence Theorem to evaluate Double intergal Z Z of S  −→F . d−→S Where −→F (x, y, z) =…

A: Given that, F=3xy2i^+xezj^+z3k^ and the surface S:y2+z2=1,x=-1,x=3

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: b) Use the Gauss-divergence Theorem to find the surface integral ff, F.n ds, where S is cylinder x²…

A: As stated in question we will use Gauss-divergence Theorem to solve this question.

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

A: Given Fx,y,z=x2i^+xyj^+zk^=Pi^+Qj^+Rk^ bounded by the coordinate planes and 3x+4y+6z=24 Hence the…

Q: 2. Use the Divergence Theorem to calculate the flux of F(x, y, z) = (x³ + y) i+(y³ + 2³) j+(z³ + x²)…

A: The given vector field is  F(x, y, z) = (x³ + y) i+ (y³ + z³) j+(x³ + x²) k across the surface of…