$\lim_{x \rightarrow -1} \frac{x+\sqrt{x^2+2x+2}}{\sqrt{3+2x}-1}$

A cura di: Administrator

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

$lim_{x rightarrow -1} frac{x+sqrt{x^2+2x+2}}{sqrt{3+2x}-1} =$

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

$lim_{x rightarrow -1} frac{x^2-x^2-2x-2}{sqrt{3+2x}-1}cdot lim_{x rightarrow -1} frac{1}{x-sqrt{x^2+2x+2}} =$

$=-frac{1}{2}cdotlim_{x rightarrow -1} frac{-2 (sqrt{3+2x}+1)}{2} = 1$