limits - Calculate $limlimits_{x to 0+}{ e^{frac{1}{x^2}}sin x}$

I want to investigate the value of $\lim_\limits{x \to 0+}{e^{\frac{1}{x^2}}\sin x}$. Since the expontial tends really fast to infinity but the sine quite slowly to 0 in comparison I believe the limit to be infinity. But I cannot find I way to prove it. I tried rewriting using the standard limit $\frac{\sin x}{x}$ as $\frac{\sin x}{x}\cdot xe^{\frac{1}{x^2}}$ but I still get an indeterminate form "$1 \cdot 0 \cdot \infty$".