Salut,
Limita din enunț are cazul de nederminare ∞ -- ∞.
Rezolvarea se regăsește mai jos:
[tex]\displaystyle \lim_{x \to +\infty}(\sqrt x-lnx)=\lim_{x \to +\infty}\sqrt x\cdot\left(1-\dfrac{lnx}{\sqrt x}\right)=\lim_{x \to +\infty}\sqrt x\cdot \lim_{x \to +\infty}\left(1-\dfrac{lnx}{\sqrt x}\right)=\\\\=+\infty+1-\lim_{x\to+\infty}\dfrac{lnx}{\sqrt x}=+\infty-\lim_{x\to+\infty}\dfrac{(lnx)\ '}{(\sqrt x)\ '}=+\infty-\lim_{x\to+\infty}\dfrac{\dfrac{1}x}{\dfrac{1}{2\sqrt x}}=\\\\\\=+\infty-\lim_{x\to+\infty}\dfrac{2\sqrt x}{x}=+\infty-\lim_{x\to+\infty}\dfrac{2}{\sqrt x}=+\infty-\dfrac{2}{+\infty}=+\infty-0=+\infty.[/tex]
Ai înțeles rezolvarea ?
Green eyes.
