Esercizi sui Limiti

  • Materia: Esercizi sui Limiti
  • Visto: 1178
  • Data: 08/05/2008
  • Di: Redazione StudentVille.it

$lim_{xto 2}((sqrt(3x-2)-sqrt(x+2))/(sqrt(x^2-3x+2)))$

esercizio svolto o teoria

A cura di: Administrator

Limite in forma indeterminata $\frac{0}{0}$

$\lim_{x \rightarrow 2} \frac{\sqrt{3x-2}-\sqrt{x+2}}{\sqrt{x^2-3x+2}} =\lim_{x \rightarrow 2} \frac{(\sqrt{3x-2}-\sqrt{x+2})(\sqrt{3x-2}+\sqrt{x+2})}{\sqrt{x^2-3x+2} (\sqrt{3x-2}+\sqrt{x+2})} =$$\lim_{x \rightarrow 2} \frac{3x-2-x-2}{\sqrt{x-2} \sqrt{x-1} (\sqrt{3x-2}+\sqrt{x+2})} = \lim_{x \rightarrow 2} \frac{2 \sqrt{x-2}}{\sqrt{x-1} (\sqrt{3x-2}+\sqrt{x+2})} = 0$