Prosiłbym bardzo o pomoc, najgorszy dział jaki mógł się trafić, a potrzebne na jutro

Nie jest taki zły. Bywają gorsze. [latex]limlimits_{x o -infty} cfrac{1-6x}{2x + 1} = limlimits_{x o -infty} cfrac{frac{1}{x} - 6}{2 + frac{1}{x}} = cfrac{-6}{2} = -3[/latex] [latex]limlimits_{x o infty} cfrac{6x^2 + x + 1}{x - 3x^2} = limlimits_{x o infty} cfrac{6 + frac{1}{x} + frac{1}{x^2}}{frac{1}{x} - 3} = cfrac{6}{-3} = -2[/latex] [latex]limlimits_{x o -infty} cfrac{5x^2 - 2x + 1}{1 - x^2} = limlimits_{x o -infty} cfrac{5 - frac{2}{x} + frac{1}{x^2}}{frac{1}{x^2} - 1} = cfrac{5}{-1} = -5[/latex] [latex]limlimits_{x o infty} cfrac{(x - 1)(1 - x)}{(1 - 6x)(x + 1)} =limlimits_{x o infty} cfrac{-x^2 + 2x - 1}{-6x^2 - 5x + 1} =limlimits_{x oinfty}cfrac{-1+frac{2}{x}-frac{1}{x^2}}{-6-frac{5}{x}+frac{1}{x^2}}=frac{1}{6}[/latex] Zad 6: a) [latex]f(x) = cfrac{1}{x^2+1}[/latex] [latex]limlimits_{x o pminfty} f(x) = limlimits_{x o pminfty} cfrac{1}{x^2+1} = 0[/latex] Asymptota: [latex]y=0[/latex] b) [latex]f(x) = cfrac{2x^2-1}{x^2+x+1}[/latex] [latex]limlimits_{x o pminfty} f(x) = 2[/latex] (obliczamy analogicznie jak wyżej) Asymptota: [latex]y = 2[/latex] c) [latex]y = -3[/latex] - asymptota d) [latex]y = 5[/latex] - asymptota e) [latex]f(x)=cfrac{sqrt{x - 4}}{sqrt{x - 1}}[/latex] [latex]limlimits_{x o infty} f(x) = limlimits_{x o infty} cfrac{sqrt{x - 4}}{sqrt{x-1}} = limlimits_{x o infty} cfrac{sqrt{1 - frac{4}{x}}}{sqrt{1 - frac{1}{x}}} = frac{1}{1} = 1[/latex] Asymptota: [latex]y = 1[/latex]