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 xf ( u, v ) = 0 and yg ( 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...
View
Full Document
 Spring '11
 NA
 Topology, Sets, Let, real continuous function, Preliminary Exam Jan, real continuous functions

Click to edit the document details