When ploting the following function $$f(x)=\frac 1x e^{x^2}(1-e^{-xe^{-x^2}})$$ we are tempted to say that $\lim\_\infty f(x)=0$ (the function is extremely close to $0$ until $10^8$ where it disappears for computer reasons), but [when computing the real limit](https://www.wolframalpha.com/input?i=limit%20%281%2Fx%29*e%5E%7Bx%5E2%7D%281-e%5E%28-xe%5E%28-x%5E2%29%29%29%20as%20x-%3Einfinity), we find $\lim\_\infty f(x)=1$. I really want to see when does the function start going to $1$ and how it starts behaving in an other way than just being constantly $0$.