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

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