Cálculo

\[\begin{array}{rcl} \lim\limits_{x \to +\infty} \sqrt{x + 1} - \sqrt{x} & = & \lim\limits_{x \to +\infty} \frac{(\sqrt{x + 1} - \sqrt{x})(\sqrt{x + 1} + \sqrt{x})}{\sqrt{x + 1} + \sqrt{x}}\\ & = & \lim\limits_{x \to +\infty} \frac{x + 1 - x}{\sqrt{x + 1} + \sqrt{x}}\\ & = & 0 \end{array}\]