hw3 - x 2 + y 2 z 2 with z 0 and below the plane z = 1-1 2...

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32B Killip Homework 3 Due Friday Apr 23 (1) From Section 16.6: 6, 12, 34, 38. (In 5th Ed, Section 16.7: 6, 10, 32, 36.) (2) Section 16.7: 20 (5th Ed: Problem 10 in Section 16.8.) (3) Section 16.8: 20 and 26 (5th Ed: Problems 6 and 22 in Section 16.8.) (4) Let T be the torus given in spherical polar coordinates by the equation ρ sin φ . (a) Draw the intersection of the torus with the plane y = 0. (I want a two dimensional sketch on axes marked ‘ x ’ and ‘ z ’.) (b) Calculate the volume of the torus. (5) Consider the region inside the cone
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Unformatted text preview: x 2 + y 2 z 2 with z 0 and below the plane z = 1-1 2 y . (a) Write the integral of f ( x,y,z ) over this region in spherical coordinates. (b) Repeat part (a) with cylindrical coordinates. (6) Compute the location of the center of mass of half of a solid sphere. Note: The rst mid-term covers the material up to and including Triple Integrals in Spherical Coordinates. See http://www.math.ucla.edu/~killip/32b/ for the order of topics. 1...
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