quiz3 - = 0 Use Implicit Function Theorem to show that f is...

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Spring 2006 Math 332 - Real Analysis II Quiz 3, 26/4/2006 Proposition: A C 1 map f : R 2 R cannot be one-to-one. We prove above Proposition using Implicit Function Theorem as follows: (a) [5] We may assume that there exists a point ( a, b ) R 2 for which Df ( a, b ) is nonsingular. Why? (b) [10] Take such a point ( a, b ) and assume f ( a, b
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Unformatted text preview: ) = 0. Use Implicit Function Theorem to show that f is not one-to-one. Justify that you can really use that theorem. (c) [5] Show that even if f ( a, b ) is never zero, one can conclude thanks to part (b) that f is not one-to-one. Ferit Ozturk, Bogazici University 2006...
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