Can I conclude that $\lim_{x\to0^+}\frac{x^2}{e^{-\frac{1}{x^2}}\cos(\frac{1}{x^2})^2}$ is infinite or it doesn't exists? $$\lim_{x\to0^+}\frac{x^2}{e^{-\frac{1}{x^2}}\cos(\frac{1}{x^2})^2}$$
My intuition is that the denominator goes to 0 faster and everything is non-negative, so the limit is positive infinity.
I cant think of elementary proof, l'Hopital doesn't help here, and I'm not sure if and how to use taylor.
WolframAlpha says it's complex infinity, but I can't understand why it doesn't just real positive infinity.
I've tried to use wolfram language to use the assumption that x is real, but couldn't get any result.

The function is not finite valued. If you allow the value $\infty$ then the limit is $\infty$. Use L'Hôpital's Rule twice to show that $\frac {e^{y}} {y^{2}} \to \infty$ as $y \to \infty$. Replace $y$ by $\frac 1 {x^{2}}$ and use the fact that $|\cos (t)| \leq 1$. 
