Compute the flux of F (x, y, z) = (y, z, x) across the surface S : R(u, v) = (u+2v, v – u, u), where u e [-1, 1] and v E [0,2].

Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u,…

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Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

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Q: Let ū = (u1, u2) be a unit vector in R? and let f: R² → R be defined by if (x, y) # (0, 0), f (x, y)…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z)=z³ i-x³j+y³ k across the sphere x² + y² +…

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Q: Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces.…

A: Step 1:- To find the flux of the vector field F=(x2+y2+z2)3/2(x,y,z)​ through the given square…

Q: Let f(x,y, z) = a² + 2y² +z² and g(x,y,z)=z-xy. Find a unit vector u satisfying D.f (1.1,2)= 0 = D,…

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Q: Is the set V = {(x, y)|x > 0} where (x1, Y1) O (x2, Y2) = (x1x2, Y1 + Y2) and c O (x, y) = (x°, cy)…

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Q: A scalar function F(x,y,z) = xy2 + x2z – z2y. Find the gradF at (1,1,1).

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: Let f(x, y) = 4x² + 5y³ A) Find the equation of the plane that passes through the point (2, -2, ƒ(2,…

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Q: Given V = {(x, y) |x>0} where (21, 31) (x2, Y2) = (x₁x2, Y₁ + y₂) and co (x, y) = (xe, cy), which…

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Q: The range of f(x,y) = 2 - x2 + 4y² is : O [0,2] O xy-plane Joo+7] O

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Q: Find the flux of F= (y, z-y, z). across the tetrahedron with vertices (0,0,0), (1,0,0), (0, 1,0),…

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Q: we look at the function f : R? → R mit f(x, y) = y sin(2x)determain the tangential plane at point…

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Q: Given that F(x, y, z) = sin(yz)i + y²j+x³k, find (i) ▼ × F (ii) ▼·F and (iii) the component of V× F…

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Q: Find a vector normal to the cylinder x2 + z2 = 8 at (2, 0, 2) by finding the gradient of the…

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Q: a) f(x, y, z) = 0 b) f(x, y, z) = 1 c) f(x, y, z) = (y + 2, z)

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