Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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2 Let S be that part of the cylindrical surface x +y 2 = 9 = 0 which lies in the first octant between the surfaces z = and z = 12 x 3* y. (a) Make a rough sketch of S. (b) Calculate the area of S using a double integral. The following steps you through it. (i) Write the cylindrical surface as F(x,y,z) = 0 and then calculate gradF. 2 x y (ii) In the expression z = substitute for either x or y. , 3 Which one is simpler? So which way will you project? Describe the region R. Decide on the order of integration. (iii) Set up the area integral and evaluate it.
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Transcribed Image Text:2 Let S be that part of the cylindrical surface x +y 2 = 9 = 0 which lies in the first octant between the surfaces z = and z = 12 x 3* y. (a) Make a rough sketch of S. (b) Calculate the area of S using a double integral. The following steps you through it. (i) Write the cylindrical surface as F(x,y,z) = 0 and then calculate gradF. 2 x y (ii) In the expression z = substitute for either x or y. , 3 Which one is simpler? So which way will you project? Describe the region R. Decide on the order of integration. (iii) Set up the area integral and evaluate it.
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