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what is $$\lim_{x\to\infty}\frac{\cosh x}{x!}?$$

I got 0 for this, as it seems $x!$ grows at a much faster rate than $\cosh x$ ?

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    When we use $x$, we usually mean the limit to be taken over all *real numbers* $x$; but $x!$ may not make sense for nonintegral $x$. If you mean to only consider integer values of $x$, then one usually signals this by using $n$ instead of $x$; that is, $$\lim_{n\to\infty}\frac{\cosh n}{n!}.$$2012-05-28
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    Of course, the factorial function *can* be extended to positive reals.2012-05-28
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    Yeah, well: also to the non-integer negative reals, but I think this is not what's being discussed here.2012-05-28

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