Given F(x, y, z) = x^2i + 2xyj + 3xzk and a region, being cut from the 1st octant by the sphere x^2 + y^2 + z^2 = 4. Sketch the region, label surfaces and find normal vectors for the surfaces.

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A: The spherical co-ordinate from a rectangular co-ordinate s given as, z=r cosϕx=rsinϕcosθy=rsinϕsinθ…

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A: Note:" Since you have posted multiple question. As per our guidelines we are supposed to solve only…

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Q: Problem III. For the bounded and shaded region, find the coordinates of the centroid.

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A: The Surface Area of the solid generated is given by,

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Q: termine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octan

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Q: 6) Find the volume of the solid in the first octant bounded by the plane 3x +4z=12, y=2 and the 3…

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Q: 4

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