oblicz granicę funkcji [latex] lim_{x o infty} 2x( sqrt{x-1} - sqrt{x+5} )[/latex]

[latex]2x(sqrt{x-1}-sqrt{x+5}) cdot frac{sqrt{x-1}+sqrt{x+5}}{sqrt{x-1}+sqrt{x+5}}= \2xfrac{x-1-x-5}{sqrt{x-1}+sqrt{x+5}}= frac{-12x}{sqrt{x-1}+sqrt{x+5}}=\frac{-12x}{x^{1/2}(sqrt{1-frac{1}{x}+sqrt{1+frac{5}{x})}}}\[/latex] [latex]=frac{-12sqrt{x}}{sqrt{1-frac{1}{x}}+sqrt{1+frac{5}{x}}} ightarrow -infty[/latex]