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Topic: Uniqueness of differential
Replies: 2   Last Post: Feb 24, 2008 12:18 PM

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Rodolfo Medina

Posts: 15
Registered: 8/21/06
Re: Uniqueness of differential
Posted: Feb 24, 2008 11:07 AM
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rodolfo.medina@gmail.com (Rodolfo Medina) wrote:

>> Sorry if this is off topic.
>>
>> 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
>> Rodolfo




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 ?




Thanks for your reply. Well, I can say that

L(P-P_0) - L'(P-P_0)
lim --------------------- = 0
P->P_0 |P-P_0|

, but this does not imply L(v) = L'(v) for all vector v. How to demonstrate
that?

Thanks,
Rodolfo




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