Use the Divergence Theorem to compute the net outward flux of the following field across the given surface S. F= ==(7y³ - 3x,5x³-4y, - 2y-4z) S is the sphere {(x,y,z): x² + y² + z² = 4}. The net outward flux across the surface is. (Type an exact answer, using * as needed.)

Q: a. Find the "Curl" of the Vector Field b. Find the "Curl" of the Vector Field when ((x,y,z) = (1, 1,…

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Q: 4. Evaluate the flux of vector field F = zi + 2yj - 2xk across part of the paraboloid z = 4-x² - y²…

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Q: 4. Let ƒ,g be C² scalar fields on R³. Verify that V x (ƒVg) = Vƒ × Vg. V × (ƒVg+gVf). V· (SVg) =…

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Q: Use the Divergence Theorem to calculate the flux of the vector fields F₁ = −4zi + 4xk and F₂ = −4zi…

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Q: Consider the vector field F(x, Y, z) = 3x?yi+ (x³ + 1) j+9z²k. Let C be the circle cut from the…

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Q: 3. Consider a square C in the xz plane of R³ with vertices (0,0,0), (1,0,0), (1,0, 1), (0,0, 1),…

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: A4. Which of the following vector fields is not the curl of another vector field? A. F=zi+=j+yk B.…

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Q: Consider the vector field F = (y, –x, x² + y²). Find the flux of F through S if: (a) S the part of…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…