Let F=[x+y, y+z, x+z] and S be a sphere of radius R. Using the divergence theorem, the value of the surface F. ndAis given by OA 47R O B. 12 7R? O c. 4 TR O D. Nothing can be said because the center of S is not given.

Q: 15. If the surface S has projection R on the xy-plane, show that F.īdS = S da dy ה.F provided |ñ -…

A: Question: If the surface S has projection R on the xy-plane, show that ∬SF¯·n¯dS=∬RF¯·n¯dxdyn¯·k¯…

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

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Q: Let the surface S in R° parametrized by f : R? - → R³, f(u, v) = (v, 2uv, (u – 1)²) Find all (u, v)…

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Q: Let F=[-x², 3y, 2xz] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: The answer is option D. Divergence theorem  Let E be a simple solid region and S is the boundary…

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 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: (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.

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Q: b) Use Gauss' theorem to evaluate f[ F· ndS where M UTM = (x² – y)i + y°z²j + (xy – y²z³)k and o is…

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Q: Use the Divergence Theorem to evaluate (4x + 9y + z2) ds where S is the sphere x2 + y2 + z? = 1.

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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: 4. For r > 0 and h > 0, show that the conical set S = (x, y, z) | x > 0, y > 0, z > 0, z2 h?(r2 - x²…

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

A: Hi, since you have asked multiple questions, we will solve the only one question for you. If want…

Q: Let S be the closed surface composed of the parabaloid z = x² + y? and the planes z =2 and z = 4.…

A: Please see the answer below.

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Q: Let F = [-x, 3y, 2xz] and S be a sphere of radius R.Using the divergence theorem, the value of the…

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Q: 6. Compute the contour integral (a) / COS Z -dz where C is the positively oriented circle |z – 1| =…

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Q: - 2 and Evaluate || curl(F)·dS where S is the portion of the top half of the sphere x +y +z? = 4…

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Q: Let C be the portion of the circle x² + y² = 4 from (2,0) to (0,2) traced counterclockwise. (a) (b)…

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A: we have surface  z=6x2+y2 and plane 6x+y+z=0lets denote the surface equation as f(x,y,z)=z-6x2-y2and…

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Q: Use the Divergence Theorem to evaluate each of the following: (a) |/ ((2x+ yz)i – 2yj + (z² + x)k) ·…

A: a) Given the field, F=2x+yzi-2yj+z2+xk The surface S is the sphere x2+y2+z2=4 with an outward…

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: Verify Stoke's Theorem for A = 3yî – xzj + yzk, where S is the surface of the paraboloid 2z = x + y?…

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

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A: We have to find the value of  ∬ F→.dS→

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: b) Use Gauss' theorem to evaluate SS F · ndS where F = (x² – y)i + y°z²j+ (xy – yz³)k and o is the…

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Q: 6. If S is the surface of the sphere x + y² + z? = 9. Prove that curl F- ds = 0. %3D

A: Solution:-

Q: Use the Divergence Theorem to evaluate F. dS where S is the sphere r² + y² + z² = 9 and F = (3r, 2y,…

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Q: Verify the divergence theorem for A = R²ag + Rsin0ag and S is the surface of a quarter of a sphere…

A: The geometry is as follows:

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Q: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

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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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Q: Evaluate J (V x F) · N dS where F = yi + (x – 2xz) j – xy k and S is the surface of the sphere x +y²…

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