Is it bad practice to use informal arguments when evaluating limits? I often see slightly informal ways of evaluating limits. For example:
$$\lim_{x\to\infty} \frac{1+\frac{\sin(x)}{x}+\frac{x}{e^x}}{3+\frac{1}{x}} = \frac{1+0+0}{3+0} =\frac{1}{3}$$
I think this is not a proof, rather a bit of an sketchy argument. 
Is it bad practice to evaluate limits like this? Or is it okay?

No, you just explain the properties used to calculate this limit: arithmetic laws, etc.
