O functie de clasa C^2 care are limita la infinit egala cu 0
Posted: Tue Mar 18, 2008 6:56 pm
Fie \( f:\(0, \infty \) \rightarrow R \) o functie de doua ori derivabila cu derivata a doua continua astfel incat \( | f^{\prime}^{\prime}(x)+2xf^{\prime}(x)+(x^{2}+1)f(x)| \leq 1 \forall x \). Aratati ca \( \lim_{x \to \infty}f(x)=0 \).
IMC Shortlist 2005
IMC Shortlist 2005