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Unformatted text preview: and real continuous functions g i ( x ) on [0 , 1] and h i ( y ) on [0 , 2] for i = 1 , . . . , n so that | f ( x, y )-n ² i =1 g i ( x ) h i ( y ) | < ± for all ( x, y ) in the rectangle. 6. Given the equations x-f ( u, v ) = 0 and y-g ( u, v ) = 0 (a) give conditions that assure you can solve for ( x, y ) in terms of ( u, v ) and (b) similarly that you can solve for ( u, v ) in terms of ( x, y ). (c) Assuming these conditions are satisﬁed prove that ∂x ( u, v ) ∂u ∂u ( x, y ) ∂x = ∂y ( u, v ) ∂v ∂v ( x, y ) ∂y 1...
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This note was uploaded on 06/19/2011 for the course MATH 600 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.
- Spring '11