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Unformatted text preview: SEAN CHEN Math5C-A1-M10-Wirts WeBWorK assignment number 5B Review is due : 07/01/2010 at 05:00am PDT. The (* replace with url for the course home page *) for the course contains the syllabus, grading policy and other information. This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TAs or your professor for help. Dont spend a lot of time guessing its not very efficient or effective. Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin ( 3 * pi / 2 ) instead of -1, e ( ln ( 2 )) instead of 2, ( 2 + tan ( 3 )) * ( 4- sin ( 5 )) 6- 7 / 8 instead of 27620.3413, etc. Heres the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. 1. (1 pt) By changing to polar coordinates, evaluate the integral ZZ D ( x 2 + y 2 ) 11 / 2 dxdy where D is the disk x 2 + y 2 16. The value is . 2. (1 pt) Using geometry, calculate the volume of the solid under z = p 4- x 2- y 2 and over the circular disk x 2 + y 2 4. 3. (1 pt) Using polar coordinates, evaluate the integral ZZ R sin ( x 2 + y 2 ) dA where R is the region 16 x 2 + y 2 36. 4. (1 pt) Find ZZ R f ( x , y ) dA where f ( x , y ) = x and R = [ 1 , 2 ] [ 2 , 5 ] . ZZ R f ( x , y ) dA = 5. (1 pt) Evaluate the double integral I = ZZ D xy dA where D is the triangular region with vertices ( , ) , ( 4 , ) , ( , 3 ) . 6. (1 pt) Match the following integrals with the verbal de- scriptions of the solids whose volumes they give. Put the letter of the verbal description to the left of the corresponding integral. 1. Z 2- 2 Z 4 + 4- x 2 4 4 x + 3 y dydx 2. Z 1 3 Z 1 2 1- 3 y 2 p 1- 4 x 2- 3 y 2 dxdy 3. Z 1 Z y y 2 4 x 2 + 3 y 2 dxdy 4. Z 1- 1 Z 1- x 2- 1- x 2 1- x 2- y 2 dydx 5. Z 2 Z 2- 2 p 4- y 2 dydx A. Solid under an elliptic paraboloid and over a planar re- gion bounded by two parabolas. B. Solid bounded by a circular paraboloid and a plane. C. One eighth of an ellipsoid. D. One half of a cylindrical rod. E. Solid under a plane and over one half of a circular disk. 7. (1 pt) Find lim ( x , y ) ( , ) x 3 y- xy 3- 8 x 3- xy or type N if the limit does not exist....
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