D

- Hướng dẫn giải

Chọn  D

$\lim \frac{2n+\sin 2n}{2n+5}=\lim \frac{2n}{2n+5}+\lim \frac{\sin 2n}{2n+5}$

Ta có $\lim \frac{2n}{2n+5}= lim\frac{2}{2 +\hspace{0.17em} {\displaystyle \frac{5}{n}}} = \frac{2}{2+\hspace{0.17em}0}=1$  và

$0\le \left|\frac{\sin 2n}{2n+5}\right|\le \frac{1}{2n+5}$ mà $\lim \frac{1}{2n+5}=0$

Suy ra $\lim \frac{\sin 2n}{2n+5}=0$ .

Vậy $\lim \frac{2n+\sin 2n}{2n+5}=1+\hspace{0.17em}0 = 1$