test3_Fall07 - 3(a Sketch the region Ω that gives rise to...

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Math 2401 M1 M2 M3 Test 3 Total: 20 points Section: Name: Student Number: 1. Determine whether or not the following vector func- tion is the gradient of a function f that is everywhere de- Fned. If so, Fnd all the functions with that gradient. (A) ( z + y sin x ) i + (1 - cos x ) j + ( x + y ) k . (2 points). (B) ( e x + x + y ) i + ( x + sin y ) j . (4 points). 2. Calculate the following double integral Z Z Ω ( x 2 + y 2 ) 1 / 3 dxdy, where Ω = { ( x, y ) : x 0 , y 0 and 1 x 2 + y 2 4 } . ( 6 points). (Hint: a coordinate change may be helpful.)
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Unformatted text preview: 3.(a) Sketch the region Ω that gives rise to the following repeated integral and change the order of integration. (4 points). Z 1-1 Z √ 1-x 2 f ( x, y ) dydx. (b)Let T be a solid bounded above by the parabolic cylinder z = 9-x 2 and below by the elliptic paraboloid z = x 2 + 4 y 2 , Fll in the blanks. (4 points). Z Z Z T dxdydz = Z 2 2 Z 2 2 Z 2 2 dydzdx. 1...
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This note was uploaded on 01/09/2009 for the course MATH 2401 taught by Professor Morley during the Fall '08 term at Georgia Tech.

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