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# tut8 - x 2 y 2 z 2 2 = 2 z x 2 y 2 4 Let F R 2 → R 2 be...

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Math 237 Tutorial 7 Problems 1: For each of the indicated regions in polar coordinates, sketch the region and then find its area. a) The region inside both r = cos θ and r = 1 - cos θ . b) The region inside r = | 1 - 4 cos θ | . 2: Convert the following equations from Cartesian coordinates to cylindrical coordinates. a) 4 z 2 = x 2 + y 2 b) x = y 3: Convert the following equations from Cartesian coordinates to spherical coordinates. a) z = x 2 + y 2 b) ( x
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Unformatted text preview: x 2 + y 2 + z 2 ) 2 = 2 z ( x 2 + y 2 ) 4: Let F : R 2 → R 2 be deﬁned by F ( u,v ) = ( ve u ,u + v ) and G : R 2 → R 2 be deﬁned by G ( x,y ) = ( x 2 y,x + 2 y ). a) Calculate D ( G ◦ F )(0 , 1) using the chain rule in matrix form. . b) Use the linear approximation of mappings to approximate the image of ( u,v ) = (0 . 01 , . 98) under G ◦ F ....
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