Use Divergence theorem to evaluate ff, F. dA, where S is the surface of the region bounded by the paraboloid z = 2 - x² - y² and the plane z = 1, and F(x, y, z) = sin(xy) - 3x²y², 2xy³-sin(xy), 3z] Ly

Q: Use the divergence theorem to calculate ff, FdS where F = x²yi - xy² j - xyz k. S is the surface of…

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Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

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Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

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Q: c) Use Stokes' theorem to evaluate where F(x, y, z) = (x²+y²z) i+(x²+xy²) j+(x²+z²) k, and C is…

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Q: Calculate F.ds where F = (3xy², xe², z³) S is the surface of the solid bounded by the cylinder y² +…

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Q: (d) In what direction does Vf point at point P? in the direction (Give a vector that points…

A: We have to find in what direction does point at point P.

Q: (x², y², z(x² + y²)) around any closed curve on the surface of Show that the circulation of F = the…

A: Circulation of vector field F around a close curve C = ∫CF.ds If parametric equation of curve C…