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June 9th, 2013, 12:56 AM  #1 
Member Joined: Apr 2013 Posts: 42 Thanks: 1  Implicit Function Theorem
Let S be described by 1. Use the implicit function theorem to determine near which points S can be described locally as the graph of a function 2. Near which points can S be described (locally) as the graph of a function ? 3. Near which points can S be described (locally) as the graph of a function? 
June 11th, 2013, 03:21 AM  #2 
Member Joined: Dec 2006 Posts: 90 Thanks: 0  Re: Implicit Function Theorem
Let . If and then 1 is satisfied. Hence 1 is true for that or . If and then 2 is satisfied. Hence 2 is true for that or . If and then 3 is satisfied. Hence 3 is true for that or . 
June 12th, 2013, 01:27 AM  #3 
Member Joined: Apr 2013 Posts: 42 Thanks: 1  Re: Implicit Function Theorem
Well, that's not so hard. But only why does lead to ? I assume as given in the theorem of the implicit function theorem? 

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