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# mm2 - [15 points Find the surface area of the part of the...

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Calculus IV [2443–004] Midterm II For full credit, give reasons for all your answers. Q1]. ..[15 points] For the double integral below, ﬁrst sketch the region of integration, and then convert it to a polar coordinares integral. Z 2 0 Z 2 y - y 2 - 2 y - y 2 f ( x,y ) dxdy Q2]. ..[15 points] Use double integrals to ﬁnd the volume of the region which is under the paraboloid z = x 2 + y 2 and above the region bounded by x = y 2 and y = x - 6. Q3].
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Unformatted text preview: ..[15 points] Find the surface area of the part of the paraboloid z = 4-x 2-y 2 which lies above the plane z = 2 and is contained in the ﬁrst octant [ie. x ≥ 0, y ≥ 0, and z ≥ 0 ]. Q4]. ..[15 points] Use the method of Lagrange Multipliers to ﬁnd the maximum and minimum values of the function f ( x,y,z ) = xyz on the sphere x 2 + y 2 + z 2 = 12....
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