ONM 2003...

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bogdanl_yex
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ONM 2003...

Post by bogdanl_yex »

Fie \( f,g:[0,\infty)\rightarrow R \), f continua, g crescatoare si nemarginita. Presupunem ca pentru orice sir \( (x_{n}) \) de numere rationale cu \( \lim_{n\to\infty}x_{n}=\infty \) avem \( \lim_{n\to\infty}f(x_{n})g(x_{n})=1 \). Sa se arate ca \( \lim_{x\to\infty}f(x)g(x)=1 \).

R. N. Gologan, ONM 2003
"Don't worry about your difficulties in mathematics; I can assure you that mine are still greater"(Albert Einstein)
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