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

A cura di: Administrator

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

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