However, see the follow up
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x*log(x) approaching y is somewhat suspicious.
I guess you’re right – there’s no guarantee that y is finite. In that case we can use Hopital’s rule. I suppose this just tells us that if the limit exists, it is zero.
That, I think, is correct. The result is still unintuitive, as log gets very small very quickly near zero.
Goes to show that relying too much on one’s intuition is something to avoid.
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