Esercizi sui Limiti

  • Materia: Esercizi sui Limiti
  • Visto: 1120
  • Data: 08/05/2008
  • Di: Redazione StudentVille.it

$lim_{xto 1}((x-sqrt(x^2-3x+3))/(sqrt(10-x)-3))$

esercizio svolto o teoria

A cura di: Administrator

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

$\lim_{x \rightarrow 1} \frac{x-\sqrt{x^2-3x+3}}{\sqrt{10-x}-3} = \lim_{x \rightarrow 1} \frac{(x-\sqrt{x^2-3x+3})\cdot (\sqrt{10-x}+3)}{(\sqrt{10-x}-3)\cdot (\sqrt{10-x}+3)} =$$\lim_{x \rightarrow 1} \frac{(x-\sqrt{x^2-3x+3})\cdot (\sqrt{10-x}+3)}{10-x-9} =$$= \lim_{x \rightarrow 1} (\sqrt{10-x}+3)\cdot \lim_{x \rightarrow 1} \frac{x-\sqrt{x^2-3x+3}}{1-x} =$$6\cdot \lim_{x \rightarrow 1} \frac{(x-\sqrt{x^2-3x+3}) (x+\sqrt{x^2-3x+3})}{(1-x) (x+\sqrt{x^2-3x+3})} =$$= 6\cdot \lim_{x \rightarrow 1} \frac{-3 (1-x)}{(1-x) (x+\sqrt{x^2-3x+3})} =$$6\cdot \frac{-3}{2} = -9$