I have to prove that f is continuous in $x_0 = 0$
$$f(x)=\frac{2x^3+x^2+x\cdot sin(x)}{(e^x-1)^2}$$
Well, if I check the limit for f it is like $\frac{0}{0} $(I have tried L'hopital but failed doing that).
Is it a good way to check if $\lim_{x \to x_0^+} = \lim_{x \to x_0^+} = L$ or is it best to use a different method here?