$\lim _{x\to 0}\left(\frac{xF\left(x\right)}{e^{x^2}}\right)$ where $F$ is a primitive function of $e^{x^2}$. 
Let $f(x)=e^{x^2}$ and F its primitive. Calculate the following limit:
$$\lim _{x\to 0}\left(\frac{xF\left(x\right)}{e^{x^2}}\right)$$

Couldn't figure this one out yet, the answer being $0$. Can I have some hints on how to approach it? Thank you.

Hint: $\lim_\limits{x\rightarrow 0} xF(x)=0$. Can you continue?
To see this, use that $F(x)=\int e^{x^2} dx$ is continuous and bounded near zero.
