Câu 1 $A=\dfrac{4.4^n + 36.6^n}{5^n+8^n}=\dfrac{4 .(\dfrac{1}{2})^n + 36. (\dfrac{3}{4})^n}{(\dfrac{5}{8})^n +1}$
Vậy $\lim A= 0$
Câu 2 $\lim (\sqrt{n^2 +2n}-n-1)=\lim \dfrac{n^2 +2n-(n+1)^2}{\sqrt{n^2+2n}+n+1}=\lim \dfrac{-1}{\sqrt{n^2+2n}+n+1} =0$
Câu 3 Ta có $\dfrac{-2}{n^2 +1} \le \dfrac{2\cos n^2}{n^2 +1} \le \dfrac{2}{n^2 +1}$
Mà $\lim \dfrac{-2}{n^2 +1} =\lim \dfrac{2}{n^2 +1} = 0$
$\Rightarrow \lim \dfrac{2\cos n^2}{n^2 +1} =0$