A cura di: Administrator

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

$lim_{xrightarrow 1} frac{2x-sqrt{5-x}}{x-sqrt{x}} = lim_{xrightarrow 1} frac{(2x-sqrt{5-x}) (x+sqrt{x})}{(x-sqrt{x}) (x+sqrt{x})} =$$lim_{xrightarrow 1} (x+sqrt{x})cdot lim_{xrightarrow 1} frac{2x-sqrt{5x}}{x (x-1)} = 2cdot lim_{xrightarrow 1} frac{(2x-sqrt{5-x}) (2x+sqrt{5-x})}{x(x-1)(2x+sqrt{5-x})}=$$2cdot lim_{xrightarrow 1} frac{4x^2-5+x}{x(x-1)(2x+sqrt{5-x})} = 2cdot lim_{xrightarrow 1} frac{4x+5}{x (2x+sqrt{5-x})} = frac{9}{2}$