Use the Divergence Theorem to calculate the surface integral ffs F- dS where F(x,y, z)= sin(y+z)i+(4x3y+ 8ylj+20x zkand S is the surface of the solid bounded by the paraboloid z = 4-x-y and the xy-plane.

Q: Let S denote the portion of the surface z=x + 4 above the triangle on the xy plane with vertices…

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Q: Calculate F· dS where F = (4x*z, 4y°z, 3:*) S is the surface of the solid bounded by the hemispheres…

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Q: Evaluate the surface integral (2ayi – yzj + zk) · dS. Where S is the part of the paraboloid z = a2 -…

A: We have to evaluate the integral ∬S2xyi^−yzj^+zxk^⋅dS where S is the path of the paraboloid…

Q: Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an…

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Q: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: C is the intersection of the cylinder with equation (x-1) + z? = 4 with the plane x + 3y +z = 9 in a…

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Q: Let I- (VxG) ndo, where G(x.y,z)=(ze*-y,4x,z*) and S is the part ofi the surface z=/x²+6y²+1 that…

A: Given that Gx,y,z=zex-y,4x,z4. The surfaces are given by z=x2+6y2+1⇒z2=x2+6y2+1 that lies inside the…