What I know
If $\lim\limits_{x \to x_0}f(x) := r$ exists, we can create a new function $\tilde f(x) = \begin{cases} f(x) &\text{if }x\in\mathbb{D}\setminus x_0 \\ r & \text{if }x = x_0 \end{cases}$ which is then the continously extended version of $f$.
What my problem is
I am struggling with $\lim\limits_{x\to 0}\frac{2x^3+x^2+x\sin(x)} {(\exp(x)-1)^2}:=r$.
I tried using L'Hôpital's rule, because I noticed that both denominator and numerator would equal to $0$ if I plug in $0$. This unfortunately didn't help at all, because you can derive those expressions as often as you want, without making your life easier.
I deliberately phrased this question in regards of solving continuity problems like this, because I think that calculating the limit in this subtask of an actual first term exam is too hard. There has to be another way of solving this continuity issue, without having to calculate the limit.
If there's no way around finding $r$, then there has to be an obvious trick that I am unaware of.
Help is greatly appreciated!