MATH 2E Quiz: MATH2E_Quiz1_2014Fall_Solutions
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Instructions: show all your work and simplify your answers completely. No calculators, notes, books, etc. may be used during the quiz. E zdv , where e is enclosed by the paraboloid z = x2 + y2 and the plane: evaluate(cid:82)(cid:82)(cid:82) z = 4. 16 (x2 + y2)da where r is the region that is of interest. You can think of it as the projection or shadow that the solid is casting down to the (x, y) plane. That region in this case is x2 + y2 = 4, or a circle of radius 2. Using polar coordinates, we have (cid:90) 2 (cid:90) 2 (cid:90) 2.
