Multivariable Calculus Quiz
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VECTORS AND GEOMETRY IN 3D
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A region is defined by 1≤x2+y2+z2≤41 \leq x^2 + y^2 + z^2 \leq 4 and x2+y2≤z2x^2 + y^2 \leq z^2 with z≥0z \geq 0. When setting up ∭Ef(x,y,z) dV\iiint_E f(x,y,z) \, dV in spherical coordinates, what is the correct range for the angle ϕ\phi and why might this be counterintuitive?
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