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Unformatted text preview: f g + g f. Prove also that 1 f =1 f 2 f, whenever f 6 = 0. 1 2 6. Suppose f is a dierentiable mapping of R into R 3 such that k f ( t ) k 2 = 1 for every t . Prove that f ( t ) f ( t ) = 0. 7. Dene f (0 , 0) = 0, and f ( x, y ) = x 2 + y 22 x 2 y4 x 6 y 2 ( x 4 + y 2 ) 2 , ( x, y ) 6 = (0 , 0) . (a) Prove, for all ( x, y ) R 2 , that 4 x 4 y 2 ( x 4 + y 2 ) 2 . Conclude that f is continuous. (b) For 0 2 , < t < , dene g ( t ) = f ( t cos , t sin ) . Show that each g has a strict local minimum at t = 0. (c) Show that (0 , 0) is not a local minimum for f ....
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 Fall '09
 Garcia
 Math

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