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

A cura di: Administrator

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

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