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# hmwk6 - integration 16.3b Do Problems 46â€“50 of Â 16.3 in...

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Math 215 Homework Set 6: §§ 15.8 – 16.5 Fall 2007 Most of the following problems are modified versions of the recommended homework problems from your text book Multivariable Calculus by James Stewart. 15.8a. Find the extreme values for the function 2 y 2 + 3 x 2 - 4 y - 2 on the set { ( x, y ) | x 2 + y 2 25 } . 15.8b. Do Problem 65 on page 983 of Stewart’s Multivariable Calculus . 16.1a. The integral D 25 - x 2 dA with D = [1 , 3] × [ - 1 , 4] represents the volume of a solid. Sketch the solid. 16.1b. Sketch the solid whose volume is given be the iterated integral 2 1 3 - 1 (15 - 3 x - 2 y ) dx dy. 16.2a. Find the volume of the bounded region in the first octant bounded by the surface z = 1+( x - 3) 2 + 3 y 2 and the planes x = 4 and y = 2 . 16.3a. In evaluating a double integral over a region D , a sum of iterated integrals was obtained as follows: D f ( x, y ) dA = 0 - 2 x - 2 f ( x, y ) dy dx + 4 0 - x - 2 f ( x, y ) dy dx.
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Unformatted text preview: integration. 16.3b. Do Problems 46â€“50 of Â§ 16.3 in Stewartâ€™s Multivariable Calculus . 16.4a. Do Problems 29â€“32 of Â§ 16.4 in Stewartâ€™s Multivariable Calculus . 16.4b. Use polar coordinates to evaluate Â± 6 Â± âˆš 36-x 2-âˆš 36-x 2 ( x 3 + y 2 x ) dy dx. 16.5a. A thin lamina is formed by considering the region inside the circle x 2 + y 2 = 6 y and outside the circle x 2 + y 2 = 9 . Find the center of mass of the lamina if the density at any point (in grams per meter squared) is inversely proportional to its distance from the origin. Follow up question: why do we not care what the constant of proportionality is?...
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