Functie compusa cu derivatele
Posted: Sat Apr 25, 2009 8:59 pm
Aratati ca nu exista functii \( f:\mathbb{R}\rightarrow\mathbb{R} \) de doua ori derivabila cu proprietatea
\( \lim_{x\to-\infty}(f\circ f^{\prime}\circ f^{\prime\prime})(x)=-\infty \) si \( \lim_{x\to-\infty}(f^{\prime\prime}\circ f^{\prime}\circ f)(x)=+\infty \)
Marius Ghergu, ,,Gh. Titeica'' 2005
\( \lim_{x\to-\infty}(f\circ f^{\prime}\circ f^{\prime\prime})(x)=-\infty \) si \( \lim_{x\to-\infty}(f^{\prime\prime}\circ f^{\prime}\circ f)(x)=+\infty \)
Marius Ghergu, ,,Gh. Titeica'' 2005