Esercizi sui Limiti

  • Materia: Esercizi sui Limiti
  • Visto: 1125
  • Data: 08/05/2008
  • Di: Redazione StudentVille.it

$lim_{xto-infty}(sqrt(x^2-3x+1)-sqrt(x^2+x-2))$

esercizio svolto o teoria

A cura di: Administrator

Limite in forma indeterminata $\infty - \infty$

$\lim_{x \rightarrow -\infty} \sqrt{x^2-3x+1}-\sqrt{x^2+x-2} =$$=\lim_{x \rightarrow -\infty} \frac{x^2-3x+1-x^2-x+2}{\sqrt{x^2-3x+1}+\sqrt{x^2+x-2}} =$$\lim_{x \rightarrow -\infty} \frac{-4x+3}{|x|\cdot \Big(\sqrt{1-\frac{3}{x}+\frac{1}{x^2}}+\sqrt{1+\frac{1}{x}-\frac{2}{x^2}}\Big)} = \text{[x < 0]} =$$\lim_{x \rightarrow -\infty} \frac{-4x+3}{-x\cdot \Big(\sqrt{1+\frac{1}{x}-\frac{2}{x^2}}+\sqrt{1-\frac{3}{x}+\frac{1}{x^2}}\Big)}=$$=\lim_{x \rightarrow -\infty} \frac{-4+\frac{3}{x}}{\sqrt{1+\frac{1}{x}-\frac{2}{x^2}}+\sqrt{1-\frac{3}{x}+\frac{1}{x^2}}} = 2$