Let S be the closed surface composed of the parabaloid z = x² + y? and the planes z =2 and z = 4. Assume S is positively oriented. Let F = (-Y, x, 2). Compute F. dS. S

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A: From Lagrange method

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

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Q: Let S be the closed surface composed of the parabaloid z = x² + y² and the planes z = 2 and z = 4.…

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Q: Let S, be the part of the paraboloid z = a² + y² that is inside the cylinder a? + y? = 1, S2 the…

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

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Q: Let h, k, m, neR such that n > m >0. A general equation corresponding to the above surface is: A) (z…

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Q: Consider the surface S given by: S :r(u, v) = (uv², u + v, v³), u E [0, 1], v E [0, 2]

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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: . Let F(x, y, z) = (x³, y³, z³). Use Gauss's theorem to find ffsF dS if S is the sphere x? + y? + 22…

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Q: (a) Given that F(x,y,z) = (3x² + 3y²)i – 2xyj + yzk, evaluate S, F·dr for which C is the boundary of…

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Q: Find the envelope of the plane 1, C + u + a + и b + u mere u is the parameter.

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Q: (b) Use Stokes' Theorem to evaluate (f, curlF .n dS, where F(x,y, 2) = x²yzi + yz?j + z³e™Yk and S…

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Q: The surface area of the part of the paraboloid z=x+y that lies under the plane z=2 is: Z=,

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Q: Consider the closed surface S consisting of the graph z = 1 - x² – y? with z 2 0, and also the unit…

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Q: Evaluate the surface integral. v² as S is the part of the sphere x2 + y2 + z2 = 64 that lies inside…

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Q: Let S denote the part of the cone x? + y = z² that lies between the planes z = 2 and z = 3+ x,…

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