Math213H-F11-midterm3-short - Math213H EXAMIII...

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Math 213H EXAM III November 16, 2011 Read each problem carefully. Show all work for each problem. No calculators or notes. 1. (16 pts) Use polar coordinates to find the area lying outside the unit circle and inside a single petal of the rose given by 2cos3 r  2. (20 pts) Use an appropriate coordinate transformation (i.e. a multiple substitution) to find the area in the 1 st quadrant enclosed by parabolas y = x 2 and y =2 x 2 and by hyperbolas xy =1 and xy =4. 3. (22 pts) Sketch and find the mass of the solid of density δ = z enclosed in the upper half plane by the cylinder 22 1 xy  , the cone 222 zxy , and the xy plane, using two different coordinate systems: a) Cylindrical coordinates b) Spherical coordinates. 4. (18pts) Sketch the vector field (, ) , ,0 Fxy y x in the x
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