$I=\lim\dfrac{5\sin n+7\cos n}{2n+1}$
$=\lim \Big( \dfrac{5\sin n}{2n+1}+\dfrac{7\cos n}{2n+1}\Big)$
Ta có:
$\Big| \dfrac{5\sin n}{2n+1}\Big|\le \dfrac{5}{2n+1}$
$\to \lim\dfrac{5\sin n}{2n+1}=\lim\dfrac{5}{2n+1}=0$
CMTT, $\lim\dfrac{7\cos n}{2n+1}=0$
$\to I=0$