Find asymptotes $e^{-x}-e^{-2x}$ I should find the asymptotes for $e^{-x}-e^{-2x}$. So I will take limits.
My attempt goes like this:
1) when x → $+\infty$ then $e^{-x}$ → $0$ and so does $e^{-2x}$. Thus: $0$. Quite easy.
2) when x → $-\infty$ then $e^{-x}$ → $\infty$ and so does $e^{-2x}$. So we have $\infty - \infty$ but the right $\infty$ is "bigger" since $e^{-2x}$ dominates over $e^{-x}$ for x close to $-\infty$.

Your analysis is correct, but absolutely not formal enough. The second case can for example be done as follows:
$$e^{-x}-e^{-2x} = e^{-x}(1-e^{-x})$$
Taking the limit $x\rightarrow-\infty$ you find a limit of the form $\infty\cdot(1-\infty)$, thus giving you $-\infty$.
