MA211Test2Solutions.pdf - MA211 Test 2 Solutions Question...

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MA211 Test 2 Solutions Question 1. [12 Marks] Let G consist of the solid above the xy -plane between the sphere x 2 + y 2 + z 2 = 16 and the plane z = 2. Fill in the missing integrand and limits of integration for the the tripple integral in cylindrical coordinates on the right hand side of the following equation: Volume of G = ˆ 2 2 ˆ 2 2 ˆ 2 2 dz dr dθ. Do not evaluate the integral.
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Question 2. [3+6+6 = 15 Marks] Let R be the region in the second quadrant enclosed by the coordinate axes and the circle x 2 + y 2 = 9. (a) Sketch the region R . Further, fill in the following limits of integration: R x y

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