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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(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. How to demonstrate that?
Thanks, Rodolfo



