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Unformatted text preview: ( x,y ) = ( x 2 + y 2 ,x 2 y 2 ) . a) Use the chain rule in matrix form to ﬁnd the derivative matrix D ( F ◦ G ). (You may leave D ( F ◦ G ) in terms of u,v,x,y ). b) Calculate D ( G ◦ F )(1 , 1). c) Use the linear approximation of mappings to approximate the image of ( u,v ) = (1 . 01 , . 98) under G ◦ F . 8. Let ( p,q ) = F ( u,v ) = (-ln( u-v ) , 1 2 ( u + v ) ) and ( u,v ) = G ( x,y ) = ( y + 1 2 e-x ,y-1 2 e-x ) . a) Find and sketch the image T of the square with vertices (0 , 0), (1 , 0), (0 , 1), and (1 , 1) under G . b) Find and sketch the image of T under F . c) Use the linear approximation of mappings to approximate the image of ( x,y ) = (0 . 01 , . 02) under F ◦ G ....
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- Fall '08
- Polar Coordinates, following equations, Polar coordinate system, Coordinate systems, following points