Let R be the disk: x²+y²<1. Then, the flux of the vector field F(x,y.z)= (x, y, 2z) across S, the portion of the surface z=1-x-y above the xy-plane, oriented by upward normals, is O None of these. x2+y²)dA J 2x? +2y² +2(1– x²?-y?)dA R. +2(1-x2-y?)dA R fex+2y-2(1-x²-y²)dA PEDMI NOTE O PRO

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Q: calculate the flux of the vector field through the given surface F = zi + (y −1)j + 5xk, and S is…

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Q: Consider the vector field Ĥ(x, y, z) = (y², x, z²). Let S3 be the portion of the paraboloid 2 = x² +…

A: Please comment if you need any clarification. if you find my answer useful please put thumbs up.…

Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

A: We have F(x,y,z)=yj-zk, S consists of paraboloid y=x2+z2, 0≤y≤1, and the disk x2+z2≤1, y=1. We have…

Q: Consider the vector field F(x, y, z) = (x, Y, 9z). Evaluate the surface integral I = ls F. dS where…

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Q: Find the flux of the vector field F(x,y,z) = xi + yj+ 2zk across o, where o is the portion of the…

A: Flux of  a vector field F on the surface S   =∫∫SF ds We will use divergence theorem  If surface S…

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Q: Consider the surface integral of the vector field F = [xy?, 3x², x²z] over a surface S, where S…

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Q: (a) Use the divergence theorem to evaluate the flux of the vector field F(x, y, z) = 0i + 4xj-2 z k…

A: We will find out the required value.

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

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Q: Use Stoke's Theorem to determine the circulation of the vector field F (x, y, z) =(3y²) î – (cos z)j…

A: Solution:  Application of Stokes Theorem.

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=&lt;x2 , -y2,…

A: The vector field is given as

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Q: Find the flux of F over the surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3 and parameterized by x =…

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A: please see the next step for solution

Q: Compute the flux of the vector field F == through the surface S where S is the surface bounded by r…

A: Given thatF→=fr,fθ,fz=r2+sin2θ,rsincosθ,3z∂∂rrfr=∂∂rr22+sin2θ=2r2+sin2θ&amp; ∂∂θfθ=∂∂θr…

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Q: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

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Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…

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Q: Find the flux of F over the surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3 and parameterized by x =…

A: Given:F(x, y, z) = x2 i+ y2 j+ z2k.Surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3Let the position…

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + y³j+ z³k put…

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Q: Evaluate the surface integral Js F · dS for the given vector field F(x,y, z) = 7xi+ 4yj+7zk and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let F = x²yi – xy'j+ (z+2)k be a vector field. Use the Diver- gence Theorem to evaluate ſſ, F ·ndS…

A: In this question, we need to find the flux of vector field by using the Gausses divergence theorem.

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Q: Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across ơ, where o is the portion of the…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: The S is composed of the surface in the paraboloid in the form y=g(x,z) f(x,y,z)=y-g(x,z)=y-x2-y2…

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A: According to our company policy, we are supposed to answer only first question. For the rest please…

Q: Evaluate the surface integral || F·dS for the vector field F(x, y,z)=3yi– 3xj+6zk where S S consists…

A: ∇F=∂ ∂xx2+y2+z2-4i+∂ ∂yx2+y2+z2-4j+∂ ∂zx2+y2+z2-4k=2xi+2yj+2zk

Q: Let S be the surface in R' that is the part of the ellipsoid 2x2 + y² + z? = 2 satisfying y > 1.…

A: In this question, we use the div.  theorem to evaluate the surface integral. given that…

Q: 3. Find the flux of the vector field F(x,y,z) = xi+ yj + 2zk across o, where o is the portion of the…

A: Find your answer below

Q: Compute the flux of the vector field F(x, y, z) = 3xj + 3yk through the surface S, where S is the…

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Q: Evaluate the surface integral F F. ds for the given vector field F and the oriented surface S. In…

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Q: Let F (x, y, z) = (y + z2, xy + ez^3, xy) be a vector field, and let S be the closed surface between…

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Q: Calculate the flux of the vector field through the given surface. F = zi + 2xj + 3yk, and S is the…

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Q: Let S be the part of the plane 2x + 2y + z = 4 which lies in the first octant, oriented upward. Use…

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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) = x³i + y³j+ z³k…

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Q: Verify Stokes Theorem for the vector field F(x,y)=(-2yz) i + y j+3x k on the part of the paraboloid…

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