Math 213HEXAM IIINovember 16, 2011Read 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 singlepetal of the rose given by2cos3r2.(20 pts)Use an appropriate coordinate transformation (i.e. a multiple substitution) to find thearea in the 1stquadrant enclosed by parabolasy=x2andy=2x2and by hyperbolasxy=1 andxy=4.3.(22 pts)Sketch and find the mass of the solid of densityδ=zenclosed in the upper half‐plane bythe cylinder221xy, the cone222zxy, and thexy‐plane, using two differentcoordinate systems:a)Cylindrical coordinatesb)Spherical coordinates.4.(18pts)Sketch the vector field(, ), ,0Fxyy xin thex‐
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Vector field, appropriate coordinate transformation, Consider vector field, line integral value