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Simple question:

If I have $\lim_{x \to -3^-}f{(x)}$ and I'm looking at a graph, am I approching -3 from the direction of +$\infty$ to -3 (as in going in the negative direction)? Or am I approaching -3 from the direction of -$\infty$ (as in the positive direction)?

edit: sorry corrected my mistake in the question.

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    $f{(x)} = \lim{x \to -3^-}$ doesn't make sense to me. Can you explain what you mean?2011-06-13
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    I assume the OP meant to write something like $\lim_{x\rightarrow -3^{-}}f(x)$, but I agree it's not clear what exactly.2011-06-13
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    I think he means $\lim_{x \to -3^{-}} f(x)$2011-06-13
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    related: http://math.stackexchange.com/questions/39826/meaning-of-lim-p-to-0/39838#398382011-06-13
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    oops. Thanks i typed up this question in a hurry.2011-06-13
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    @Chandru: Yes, it looks like that question came first, but this one is really the more general one. There might be an argument for keeping them both open, I'm not sure.2011-06-13
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    @Zev: Me too! That's why I put related and not duplicate.2011-06-13

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"$\displaystyle\lim_{x\rightarrow-3^{-}}$" denotes approaching $-3$ from the left (i.e. from $-\infty$), to the right (i.e. in the positive direction). The Wikipedia page on one-sided limits helps clear things up a bit.

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    Ok, thanks, that helped a lot :).2011-06-13
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If you find the $\lim_{x\to -3-} f(x)$ notation confusing, you can also write $$\lim_{x\uparrow -3} f(x)$$ and think, "this is the limit of $f(x)$ as $x$ increases toward $-3$." Likewise, you can use $$\lim_{x\downarrow-3} f(x)$$ to denote the right-hand limit.

I readily concede that is a matter of taste, but matters of taste such as this one affect readability, and that's important.