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I have two functions f(x) and g(x), and I am trying to take the limit of f(x)/g(x):

$\lim_{x\to ∞} f(x)/g(x)$

The value of f(x) is a constant (greater than 0) and after substituting infinity into g(x), I got 0. Since the denominator is 0, does this mean that the limit does not exist?

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    $\begingroup$ Not necessarily: $\lim_{x\to\infty}\frac{1}{e^{-x}}=\infty$. $\endgroup$
    – egreg
    Mar 11, 2019 at 0:12

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This is the sort of thing that not all texts agree on. What I mean by that is that some texts treat infinite limits as "not existing", whereas others would write (as @egreg has in the comments) that the limit is infinity (or negative infinity, as the case may be). Based on what you have written (without further details), I suspect that yours is a limit that goes to infinity, which in some sense exists, depending on how comfortable you are with infinities.

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