Giải thích các bước giải:
Ta có :
$L=\lim\dfrac{3n+1+\sin n}{2n+5}$
$\to L=\lim\dfrac{3n+1}{2n+5}+\dfrac{\sin n}{2n+5}$
$\to L=\lim\dfrac{3+\dfrac 1n}{2+\dfrac 5n}+\dfrac{\sin n}{2n+5}$
$\to L=\lim\dfrac 32+\dfrac{\sin n}{2n+5}$
$\to L=\dfrac 32+\lim\dfrac{\sin n}{2n+5}$
Mà $A=\lim\dfrac{\sin n}{2n+5}$
$\to |A|=\lim|\dfrac{\sin n}{2n+5}|$
$\to 0\le |A|=\lim|\dfrac{\sin n}{2n+5}|\le \lim|\dfrac{1}{2n+5}|$
$\to 0\le |A|\le 0$
$\to A=0$
$\to L=\dfrac 32$
