I'm struggling with this limit, tried everything on it but can't treat this indeterminate form... 

$$ \lim\_{x\rightarrow 0} \frac{\sin\frac{1}{x}}{e^{\frac{1}{x}} + 1}$$

Ideally, I want to evaluate it using a change of variables, but every other method would be most welcome.

I thank you guys for your explanation and your help.