L'Hopital's Rule seemingly not giving graphical result

L'Hopital's Rule assumes that $\lim \frac {f'(x)} {g'(x)}$ exists and then proves that $\lim \frac {f(x)} {g(x)}$ exist and the two limit are equal. The rule is not applicable here.

L'Hôpital's rule states that, for limits of the form $0/0$ and $\infty/\infty$, we have: $$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)},$$ if the latter limit exists. In this case it does not, and so L'Hôpital's rule does not help us to reach any conclusions.