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Unformatted text preview: ± u v ² = ± 1 2 3 ²± x y ² , ± x y ² = 1 3 ± 32 1 ²± u v ² = 1 3 ± 3 u2 v v ² . That is, x = (3 u2 v ) / 3 and y = v/ 3 . ( * ) Now it is easy: We just substitute these expressions into the three equations for the three given sets S . (a) The equation for the yaxis is x = 0. Using ( * ) to express this in terms of u and v , we get (3 u = 2 v ) = 0, or, what is the same, v = 3 2 u . (This the the equation of the line through the origin in the u, v plane with slope 3 / 2.) (b) As in part (a) , we use ( * ) to express the equation for S , here x + y = 3, in terms of u and v . The result is: (3 u2 v ) / 3 + v/ 3 = 3 , which simpliﬁes to v = 3 u9 , 21 /september/ 2005; 22:09 45...
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.
 Fall '08
 Gladue
 Calculus, Unit Circle

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