Originally Posted by

**johnsomeone** With this kind of limit, I like to first note which factors are relevant. That (3+sin(x)) part isn't - it's going to 3, so isn't going to be the cause of the limit converging or not. The other two factors are what count. As a hint, when it's "like 0/0", and has x's and sin(x)'s and is a limiti as x goes to 0, almost surely you'll end up using sin(x)/x goes to 1 as x goes to 0.

As a hint, note that

$\displaystyle \frac{x^2}{(x+\sin(x))^2} = \left(\frac{x}{x+\sin(x)}\right)^2 = \left(\frac{1}{1+\frac{\sin(x)}{x}}\right)^2$