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Given S is a surface for a part of the sphere x y z 4...

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Calculus

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Given S is a surface for a part of the sphere x y z 4 that lies above the cone z x y Find a parametric representation for the surface S in term of o and 8 Then determine the domain of and 0 Based on the expression written previously show that rx rell 4 sin o Hence compute the surface integral of ffs ds where the surface S is given parametrically by r 0 0 Let C is the boundary curve along the bottom of the upper half of the sphere thus use Stokes theorem to compute the line integral of fo F dr where F x y z xzi yzj xyk and upwards orientation

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