prf - 1 Mathematics 23B; Fall 2008; V. Ginzburg Practice...

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Unformatted text preview: 1 Mathematics 23B; Fall 2008; V. Ginzburg Practice Final 1. For each of the ten questions below, state whether the assertion is true or false . (You do not need to justify your answer.) (a) The area of the portion of the graph of z = f ( x,y ) over a region D in the ( xy )-plane is equal to ZZ D s 1 + f x 2 + f y 2 dA. (b) Let be the region in R 3 bounded by a surface S and F a C 1 vector field in R 3 . Gauss theorem asserts that ZZZ F dV = ZZ S F d S , where S is oriented inward. (c) Let S be the unit sphere. Then RR S x 2 z dS = 0. (d) Let z , r , and be cylindrical coordinates. Then ( x,y,z ) ( r,,z ) = r 2 sin . (e) Every onto map is necessarily one-to-one. (f) The integral RR S f dS , where f is a function, changes sign when the orien- tation of S is changed. (g) Let D be the region to which Greens theorem applies. Then the area of D is equal to 1 2 R D ( xdy- ydx )....
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This note was uploaded on 12/16/2010 for the course MATH 100 taught by Professor Jim during the Spring '10 term at American Jewish University.

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prf - 1 Mathematics 23B; Fall 2008; V. Ginzburg Practice...

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