$lim_{xto+infty}(x(sqrt(x+1)-sqrtx))$

A cura di: Administrator

Limite in forma indeterminata $infty-infty$

$lim_{xrightarrow +infty} xcdot (sqrt{x+1}-sqrt{x}) = lim_{xrightarrow +infty} xcdot frac{x+1-x}{sqrt{x+1}+sqrt{x}} =$$lim_{xrightarrow +infty} frac{x}{sqrt{x}cdot (sqrt{1+frac{1}{x}}+1)} = +infty$