F97_Final_Exam-G.Bergman

F97_Final_Exam-G.Bergman - I 0 / 0 5 / 2 O 0 I F R I 1 0 :...

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Unformatted text preview: I 0 / 0 5 / 2 O 0 I F R I 1 0 : 1 9 F A X 6 4 8 4 A 8 0 George M. Bergman 145 Dwinelle ilOFFITT LIBRARY Fall 1997, Math 53M Final Exam @ o o r 18 December. 1997 8:00-l l:00 AM 1. (+S points, 5 points apiece) Give each of the following if it is defined. If an expression is undefined, say so. (You do not have to give a reason in such cases.) (a) An equation for the tangent plane to the surface t? - zyz + 322 = 2o at the point ( 1 , 2 , 3 \ . (b) An expression to, lj=o !{!_nfU,ildye in which the orderof integrations is reversed (i.e., as an iteratcd intcgral of f(x,/) in which the outer integration is with respect to y and the inner integration with respect to .r). (c) Themassof alaminaoccupyingthequarter-circularregion l(x,y) l,rZ0,y)0, ,2 +y2< l), and having dcnsity function p(x,y) = xy. (d) A sketch of the curve x= sin2t, y= sinf, 0<t<2n, withthe maximum and minimum values of r and y marked on the axes....
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F97_Final_Exam-G.Bergman - I 0 / 0 5 / 2 O 0 I F R I 1 0 :...

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