Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: Uniqueness of differential
Posted:
Feb 24, 2008 11:07 AM
|
|
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
|
|
|
|
