Oblicz Granice : a)[latex] lim_{n o infty} (n- sqrt{n^{2} +2n)[/latex] b)[latex] lim_{x o 3} frac{x^{2}-9 }{x-3} [/latex]

[latex]lim_{n oinfty}(n-sqrt{n^2+2n})=lim_{n oinfty}frac{n^2-n^2-2n}{n+sqrt{n^2+2n}}=\=lim_{n oinfty}frac{-2n}{n(1+sqrt{1+frac{2}{n}})}=lim_{n oinfty}-frac{2}{1+sqrt{1+frac{2}{n}}}=-frac{2}{1+1}=-1[/latex] [latex]lim_{x o3}frac{x^2-9}{x-3}=lim_{x o3}frac{(x-3)(x+3)}{x-3}=\=lim_{x o3}(x+3)=3+3=6[/latex]