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MIT OpenCourseWare 18.02 Multivariable Calculus Fall 2007 For information about citing these materials or our Terms of Use, visit: .
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18.02 Practice Exam 48 Problem 1. (10 poir~ts) Let C 1)e the portion of the cylinder z2 + y2 2 1lying in the fi~t octant (:L 2 0, y 2 0, z 2 0) and 1)elow t,he plane z = 1. Set 1111 a triple integral in cglCri,i.rlr(ctr.l coo~r.rlCri,i.ates which gives the monierlt of inertia of C a1)olit the z-axis; assnine the density to 1)e 15 = 1. (Give integrancl and limits of integration, l~lit do not ~ln1,i~ate.) Problem 2. (20 poir~ts: 5; 5, 10) a) A solid sphere S of radins a is place(1 a1)ove the :cy-plane so it is tangent, at the origin and its diameter lies along the z-axis. Give its eqiiation in sl~he~ical: coor.(iinntrs. 1)) Give the equation of the horizontal plane z = n in spherical coordinates. c) Set 111) a triple integral in spherical coordinates whid~ gives the vohinie of the portion of the sphere S lying abolie the plane z = a. (Give integrami and limits of integr;ltion, 1)iit (lo not
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prac4b - MIT OpenCourseWare http:/ 18.02...

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