User talk:Noegenesis

Edit to Frechet derivative

This edit summary was incorrect. You can check the formula that was in the article by a direct calculation:

\lim _{t\to 0}{\frac {1}{t}}\left({\frac {t^{3}a^{2}b}{t^{4}a^{4}+t^{2}b^{2}}}\right)={\frac {a^{2}}{b}}

for $b\not =0$ . Moreover, in the example that you replaced this with, the Gateaux derivative at (0,0) fails to exist in any direction (except where ab=0), which is not what you wrote, nor is it relevant to the point being made in the text. siℓℓy rabbit (talk) 20:24, 17 October 2008 (UTC)[reply]

Wow, I was idiotic enough to forget the \frac{1}{t} factor in the limit, which is what led me to these incorrect conclusions. Thanks for correcting my mistake! Noegenesis (talk) 12:19, 18 October 2008 (UTC)[reply]