O functie de clasa C^2 care are limita la infinit egala cu 0

Moderators: Bogdan Posa, Laurian Filip, Beniamin Bogosel, Radu Titiu, Marius Dragoi

Post Reply
User avatar
bogdanl_yex
Pitagora
Posts: 91
Joined: Thu Jan 31, 2008 9:58 pm
Location: Bucuresti

O functie de clasa C^2 care are limita la infinit egala cu 0

Post by bogdanl_yex »

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
"Don't worry about your difficulties in mathematics; I can assure you that mine are still greater"(Albert Einstein)
Top
Post Reply

Return to “Analiza matematica”