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.

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.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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