Asymptotic expansion of $\exp(-\frac{1}{\epsilon^2+\epsilon^3})$ I am trying to find the asymptotic approximation of $\exp(-\frac{1}{\epsilon^2+\epsilon^3})$.
I reformed it into $\frac{\exp(\frac{1}{\epsilon})}{\exp(\frac{1}{\epsilon^2})\exp(\frac{1}{1+\epsilon})}$ so I can now Taylor expand $\exp(\frac{1}{1+\epsilon})$ but haven't got any further with the other two.
I also wasn't able to derive the expansion using integration by parts because I can't evaluate the expression when $\epsilon$ is 0.
Any hints would be appreciated!

We have
\begin{align*}
\exp \left( { - \frac{1}{{\varepsilon ^2  + \varepsilon ^3 }}} \right) &= \exp \left( { - \frac{1}{{\varepsilon ^2 }}\frac{1}{{1 + \varepsilon }}} \right) = \exp \left( { - \frac{1}{{\varepsilon ^2 }}\left( {1 - \varepsilon  + \varepsilon ^2  + \mathcal{O}(\varepsilon ^3 )} \right)} \right)
\\ & = \exp \left( { - \frac{1}{{\varepsilon ^2 }} + \frac{1}{\varepsilon } - 1 + \mathcal{O}(\varepsilon )} \right) = \exp \left( { - \frac{1}{{\varepsilon ^2 }} + \frac{1}{\varepsilon } - 1} \right)(1 + \mathcal{O}(\varepsilon )),
\end{align*}
as $\varepsilon \to 0$.
