Question

Cazul ∞-∞, diferenta de radicali, limita la +-∞, cu amplificare cu conjugata:
lim (x->∞) ($(\sqrt{x^2+1}-x)$

Answer 1

$\lim_{x \to \infty} ( \sqrt{x^2+1}-x)$
Amplificam cu conjugata , adica cu $\sqrt{x^2+1}+x$
Obtinem :$\lim_{x \to \infty} \frac{ ( \sqrt{x^2+1}-x)( \sqrt{x^2+1}+x) }{ \sqrt{x^2+1}+x }= \lim_{x \to \infty} \frac{x^2+1-x^2}{ \sqrt{x^2+1}+x } = \frac{1}{ \sqrt{x^2+1}+x } =0$