Salut,
Uite soluția corectă:
[tex]\lim\limits_{x\to -\infty}[x(\sqrt{9x^2+5}+3x)].\ Not\breve{a}m\ x=-p,\ deci\ p\to+\infty.\ Limita\ devine:\\\\\lim\limits_{p\to +\infty}\left[-p\left(\sqrt{9p^2+5}-3p\right)\right]=\lim\limits_{p\to +\infty}\left[-p\dfrac{\left(\sqrt{9p^2+5}-3p\right)\left(\sqrt{9p^2+5}+3p\right)}{\sqrt{9p^2+5}+3p}\right]=\\\\=\lim\limits_{p\to +\infty}\left[-p\dfrac{9p^2+5-9p^2}{\sqrt{9p^2+5}+3p}\right]=\lim\limits_{p\to +\infty}\left[-p\dfrac{5}{\sqrt{p^2\cdot\left(9+\dfrac{5}{p^2}\right)}+3p}\right]=\\\\\\=\lim\limits_{p\to +\infty}\left[-p\dfrac{5}{|p|\sqrt{9+\dfrac{5}{p^2}}+3p}\right]=\lim\limits_{p\to +\infty}\left[-p\dfrac{5}{p\sqrt{9+\dfrac{5}{p^2}}+3p}\right]=\\\\\\=\lim\limits_{p\to +\infty}\left[\dfrac{-5}{\sqrt{9+\dfrac{5}{p^2}}+3}\right]=\dfrac{-5}{\sqrt9+3}=-\dfrac{5}6.[/tex]
Green eyes.
