# a8 - 4 Let p q = F u v = v cos uv 2 v √ u 2 5 and u v = G...

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Math 237 Assignment 8 Due: Friday, Nov 19th 1. For each of the indicated regions in polar coordinates, sketch the region and ﬁnd the area. a) The region enclosed by r = cos 2 θ . b) Inside r = 3 cos θ and outside r = 1 + cos θ . 2. Let T ( x, y ) = ( x + 2 y, 3 x - y ) and let D = { ( x, y ) R 2 | - 1 x 2 , 0 y 2 } . Find the image of D under T . 3. Let T ( x, y ) = ( x 2 + y 2 , x 2 - y 2 ) and let D = { ( x, y ) R 2 | 1 x 2 , 0 y 2 } . Find the image of D under T .
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Unformatted text preview: 4. Let ( p, q ) = F ( u, v ) = ( v cos( uv + 2) , v √ u 2 + 5 ) and ( u, v ) = G ( x, y ) = ( xy-xy 2 , xe xy-2 ). a) Use the chain rule in matrix form to ﬁnd 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 ....
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