/sci/ - Science & Math

I need to know how to go about solving this (and problems of this kind):

Find <span class="math">a[/spoiler] so that the limit exists and is finite: <span class="math">\lim_{x\rightarrow 0 }\frac{e^{x}-e^{-x}+ax}{x-sin x}[/spoiler]

I know the answer is -2, I'm just looking for THE way to solve these, if there's one.

I did L'Hopital and deduced <span class="math">a[/spoiler] had to be -2 from what I got, but that can't be how you solve these.

embarrassing moments in your college class:

>have presentation in biology
>go through presentation, all good
>teacher asks to go back to a slide
>noticed that I accidentally put that viruses build resistance to antibiotics
>mf
>"oops I was just saying infections in general"
>mfw the next presentations were way worse of a trainwreck