hmwk5 - z = 1 x-3 2 3 y 2 and the planes x = 4 and y = 2...

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Math 215 Homework Set 5: §§ 15.8 – 16.3 Winter 2008 Most of the following problems are modified versions of 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 - 3 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
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Unformatted text preview: 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 = ±-2 ± x-2 f ( x, y ) dy dx + ± 4 ±-√ x-2 f ( x, y ) dy dx. Sketch the region and express the double integral as an iterated integral with reversed order of integration. 16.3b. Do Problems 46–50 of § 16.3 in Stewart’s Multivariable Calculus ....
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