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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.

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

$$ e^{-x}=\frac1{e^x} $$

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  • $\begingroup$ Wow. Hah. Thank you. I'm surprised i didn't notice such a fundamental explanation. $\endgroup$ – Ulad Kasach Aug 31 '15 at 14:46
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The guiding question goes like this: What happens when you divide $1$ by a really, really large number?

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Have a look at the graph:

enter image description here

Notice what happens when you go from a negative number to a positive number.

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