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Unformatted text preview: . 1 2) The function G of the hint satises the condition G ( x ,y ) = 0. Furthermore G y ( x ,y ) = 1 /g ( y ) 6 = 0 . Under these conditions the implicit-function theorem guarantees that there exists a unique solution y = ( x ) of the equation G ( x,y ) = 0 reducing to y when x = x , in a suciently small neighborhood of x . 5) The right-hand side is homogenous of degree zero and the so-lution, with y = xv , is given implicitly by Z v ds a + bs c + ds-s = ln x. 10) Since by assumption ( pM ) y = ( pN ) x and ( qM ) y = ( qM ) y it follows immediately that the same relation holds with p + q in place of p or q . 2...
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This note was uploaded on 09/29/2011 for the course COMM 150 taught by Professor Jordan during the Spring '99 term at Pennsylvania State University, University Park.
- Spring '99