Oblicz granice [latex]1000 lim_{x o infty} sqrt{ 4x^{2}+x+1 } [/latex] -2x

[latex]displaystyle 1000lim_{x o infty}left(sqrt{4x^2+x+1}-2x ight)=\ 1000lim_{x o infty}left(sqrt{4x^2+x+1}-2x ight)cdotdfrac{sqrt{4x^2+x+1}+2x}{sqrt{4x^2+x+1}+2x}=\ 1000lim_{x o infty}dfrac{4x^2+x+1-4x^2}{sqrt{4x^2+x+1}+2x}=\ 1000lim_{x o infty}dfrac{x+1}{sqrt{x^2left(4+dfrac{1}{x}+dfrac{1}{x^2} ight)}+2x}=\ 1000lim_{x o infty}dfrac{xleft(1+dfrac{1}{x} ight)}{xsqrt{4+dfrac{1}{x}+dfrac{1}{x^2}}+2x}=[/latex] [latex]displaystyle1000lim_{x o infty}dfrac{xleft(1+dfrac{1}{x} ight)}{xleft(sqrt{4+dfrac{1}{x}+dfrac{1}{x^2}}+2 ight)}=\ 1000lim_{x o infty}dfrac{1+dfrac{1}{x}}{sqrt{4+dfrac{1}{x}+dfrac{1}{x^2}}+2}=\ 1000cdotdfrac{1+0}{sqrt{4+0+0}+2}=\ 1000cdotdfrac{1}{sqrt{4}+2}=\ 1000cdotdfrac{1}{4}=\ 250 [/latex]