solutions to the calculus and linear algebra problems on the comprehensive examination of february 3 2006 solutions to problems 1 4 and 8 are omitted since they involve topics no ...
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...Solutions to the calculus and linear algebra problems on comprehensive examination of february are omitted since they involve topics no longer covered find volume region in dimensional space inside cylinder x y above xy plane below z solution we ll be working with cylindrical coordinates here constraint is pretty obvious it just means that r other two constraints bound rcos note so this a legitimate inequality for problem v zzz dv zv rdzd dr d sin rsin rdr consider function f if compute use denition partial derivative symmetric respect switching only need one calculation h lim b prove not dierentiable at will dierentiability new comps let t dt nding remember fundamental theorem g rest straightforward dy i j bi show saddle point second test det...