Esercizi sui Limiti

  • Materia: Esercizi sui Limiti
  • Visto: 1294
  • Data: 08/05/2008
  • Di: Redazione StudentVille.it

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

esercizio svolto o teoria

A cura di: Administrator

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

$\lim_{x \rightarrow 3} \frac{\sqrt{2x+3}-3}{\sqrt{x+1}-2}=\lim_{x \rightarrow 3} \frac{(\sqrt{2x+3}-3) (\sqrt{x+1}+2)}{(\sqrt{x+1}-2) (\sqrt{x+1}+2)} =$$\lim_{x \rightarrow 3} (\sqrt{x+1} +2)\cdot \lim_{x \rightarrow 3} \frac{\sqrt{2x+3}-3}{x+1-4} = 4\cdot \lim_{x \rightarrow 3} \frac{(\sqrt{2x+3}-3) (\sqrt{2x+3}+3)}{(x-3) (\sqrt{2x+3}+3)} =$$4\lim_{x \rightarrow 3} \frac{2 (x-3)}{(x-3) (\sqrt{2x+3}+3)} = \frac{8}{6} = \frac{4}{3}$