Question

lim x²/ √x²+12 - √12 qndo x tende a 0

Answer 1

$\\ \lim_{x \to 0} \frac{x^2}{\sqrt{x^2 + 12} - \sqrt{12}} \times \frac{\sqrt{x^2 + 12} + \sqrt{12}}{\sqrt{x^2 + 12} + \sqrt{12}} = \\\\\\ \lim_{x \to 0} \frac{x^2(\sqrt{x^2 + 12} + \sqrt{12})}{x^2 + 12 - 12} = \\\\\\ \lim_{x \to 0} \frac{x^2(\sqrt{x^2 + 12} + \sqrt{12})}{x^2} = \\\\\\ \lim_{x \to 0} \frac{\sqrt{x^2 + 12} + \sqrt{12}}{1} = \\\\\\ \boxed{2\sqrt{12}}$