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Unformatted text preview: 1) 2 ] if 0 x 1 and 0 y 1. 6. Prove that if all the second partial derivatives of f are continuous at a point ( a,b ) then f x , f y and f are all continuous at ( a,b ). 7. Find a function f ( x,y ) such that f xy (0 , 0) and f yx (0 , 0) both exist, but f xy (0 , 0) 6 = f yx (0 , 0). Prove you are correct. 8. Consider f : R 2 R dened by f ( x,y ) = 2 x 2 + 3 y 2 . Prove that for any ( a,b ) R 2 we have f ( x,y ) L ( a,b ) ( x,y ) for all ( x,y ) R 2 ....
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This note was uploaded on 04/18/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.
 Spring '08
 WOLCZUK
 Math, Chain Rule, The Chain Rule

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