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Unformatted text preview: First we show that Equation ( 3.17 ) determines a well-dened function ( x ): For notational convenience, we assume without loss of generality that f ( x ,y ) = 0 (that is, c = 0), and f y ( x ,y ) > . Since f ( x,y ) is continuous, we know that f y ( x ) > 0 at all points x = ( x,y ) suciently near x , say for | x x | and | y y | 2 . For any a [ x ,x + ], consider the function of y obtained by xing the value of x at x = a : g a ( y ) = f ( a,y ) ;...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08