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Re: Uniqueness of differential
Posted:
Feb 27, 2008 1:35 PM


rodolfo.medina@gmail.com (Rodolfo Medina) writes:
>>> Can anybody suggest a proper place to ask the following question: >>> how to demonstrate the uniqueness of the differential of a function? >>> Given a function f, its differential in P_0 is a linear map L such that >>> >>> lim f(P)  f(P_0)  L(P_0  P) >>> P>P_0  = 0 >>> P_0  P >>> >>> >>> Thanks for any indication
Christopher Henrich <chenrich@monmouth.com> writes:
>> This has a "homework" look to it, so, here is a leading question. >> >> Suppose that, given L as above, there is another linear map L' >> satisfying a similar equation. Can you say anything about L'  L ?
Rodolfo:
> Thanks for your reply. Well, I can say that > > L(PP_0)  L'(PP_0) > lim  = 0 > P>P_0 PP_0 > >, but this does not imply L(v) = L'(v) for all vector v.
Christopher Henrich <chenrich@monmouth.com> writes:
> Suppose that for some v L(v) /= L'(v). Consider P on the line through P_0 > that is parallel to the vector v.
This makes me think that P_0 is supposed to be internal to the set  let's call it X  where f is defined. Isn't it possible to do without this hypothese?
Thanks Rodolfo



