alculate the surface integral ff F. NdS, where F = S (u, v) = (uv, v, u) where 0 ≤ u ≤ 4, 0 ≤ v ≤ 3. nter an exact answer. rovide your answer below: Flux (3xy, -3yz, -4xz) and S is the surface with parameterization

Q: Use a graphing utility to sketch and describe the surface

A: (7) In the graphing utility, just write the equation, x216+y225+z225=1. Plotted 3D graph will look…

Q: Evaluate the surface integral G(x,y,z) do using a parametric description of the surface. 2 2…

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Q: Verify Stokes's Theorem for F = z?i + x²j + y?k and S is the surface z? = x² + y?, y 2 0, %3D and 0…

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Q: A parametric representation of the surface y? + z² – x² = 0 in R³ is given by, Select one: O a. æ =…

A: option (b) is correct.

Q: I. Evaluate '9 + 3z°dS for the surface S defined by S r(u, v) = [6 cos(u) sin(v), 6 sin(u) sin(v), 3…

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Q: S Ⓒ Directly evaluate SS F(x, y, z)=-yi₁ +x¾-2K^, where s is the surface 2 = x² + y², for 0≤²≤4. Joo…

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Q: Please

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Q: Classify all critical points for the surface flaiy)= 2x-y-2xy.

A: We have to classify all the critical points for the surface…

Q: Find the flux of F (x, y, z) = 4.xi+ 4yj+ 2k outward (away from the z-axis) through the surface cut…

A: The field lines of a vector field F through surfaces with unit normal n, the angle from n to F is θ.…

Q: Consider the surface with parametrization 7 (u, v) = (u, v, u² – v²). Fill in the blank to find the…

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Q: Evaluate the surface integral: S Ssx*y ds Where S is the surface of the paraboloid z = 4 – x2 – y?…

A: To evaluate the given surface integral, use the following formula. ∬SFx,ydS=∬DFx,y1+∂z∂x2+∂z∂y2dxdy

Q: Compute the flux of F = (5(z + 2), 5, 52) through the surface S given by y = ² + 2, with 0 0, z 2 0,…

A: We have to find flux.

Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + z² = 1 that lies above…

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Q: Let F = yi+zj + xk and C is the boundary of the surface S, which is the paraboloid z = 1 - (x² +…

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Q: Evaluate F dS, S where 4 F(x, y, z) = (3y, -2x, -), and S is the surface that is composed of the…

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Q: Consider the surface described by the equation x³ +y³ + z³ = xyz = 1. a. Check that this surface can…

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Q: Example 3. Let S be the surface z=1-2²-y², z 20. Evaluate the surface integral: [2√5-12 ds

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Q: Evaluate the surface integral. 116x² S is the part of the sphere x² + y² + z² = 36 that lies inside…

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Q: SET UP the surface integral ffxz dS where S is the part of the surface x=4-y²-2² in front of the…

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Q: Consider the surface S:z=4e - 4xy, with P(0,1,1) beng a pont of S. The equation of the tangent lime…

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Q: 2. Calculate the surface integral / G(r) dA, where G = (12zz + 36)1/2, the surface S is given by the…

A: We will use  ∫∫Sfx,y,zdS=∫∫Dfru,v.ru×rvdA

Q: Given a function f (x, y) = /4 + 2x – 4y – x² – y².

A: The given function is:fx, y=4+2x-4y-x2-y2