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June 9th, 2013, 12:56 AM   #1
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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?
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June 11th, 2013, 03:21 AM   #2
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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 .
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June 12th, 2013, 01:27 AM   #3
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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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