# Why does $e^{-x}$ approach $0$ as $x$ gets large? [closed]

Why is it that

$$\lim_{x \to -\infty} e^x = 0?$$

Context: College has started back up again and I like to understand the reasons why things do the things they do, rather than just memorizing. I'm sure i've seen it before - but I am coming up with a blank today.

• Graph the function out that will show you. – Arjun Dhiman Aug 29 '15 at 21:04
• This is easier if you think about it with $10$ instead of $e$. $10^{-100}=0.000\dots001$ is very small, right? – Akiva Weinberger Aug 30 '15 at 5:45

$$e^{-x}=\frac1{e^x}$$
The guiding question goes like this: What happens when you divide $1$ by a really, really large number?