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Unformatted text preview: a) The region enclosed by r = cos 2 . b) Inside r = 3 cos and outside r = 1 + cos . 7. Let T ( x,y ) = ( x + 2 y, 3 xy ) and let D = { ( x,y ) R 2  1 x 2 , y 2 } . Find the image of D under T . 8. Let T ( x,y ) = ( x 2 + y 2 ,x 2y 2 ) and let D = { ( x,y ) R 2  1 x 2 , y 2 } . Find the image of D under T . 9. Let ( p,q ) = F ( u,v ) = ( v cos( uv + 2) ,v u 2 + 5 ) and ( u,v ) = G ( x,y ) = ( xyxy 2 ,xe xy2 ). a) Use the chain rule in matrix form to nd D ( F G )(1 , 2). b) Use the linear approximation for mappings to approximate the image of ( x,y ) = (1 . 1 , 1 . 9) under F G . NOTE: Only * questions will be graded...
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This note was uploaded on 12/05/2011 for the course MATH 237 taught by Professor Wolczuk during the Winter '08 term at Waterloo.
 Winter '08
 WOLCZUK
 Calculus, Polar Coordinates

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