I don't know how to solve the following limit without using series expansion.
$$\lim_{x\to 0} \frac{(1+x)^x -1 -x^2}{x^3} $$
I have tried use L'Hopital's rule and finding bounds to use squeeze theorem but to no avail. Please give me hints on how to compute the limit, instead of posting full answers. Thanks in advance :)
Edit: I have just found an answer, though it is not elegant at all. It is done simply by applying L'Hopital's rule three times and there is not much to say about it. Still, other answers are welcome.