Which is bigger
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Brenden Tran
Answered question
2022-06-24
Which is bigger or I'm trying to find out which is bigger or as I tried to take the log of both but I didnt't reach any where.
Answer & Explanation
Jayce Bates
Beginner2022-06-25Added 18 answers
You can try to take . To do that, see that:
and so you have to compare and . So take
This equals
which is a much easier limit to analyse. Applying l'Hôpital's rule to the fraction inside the parentheses we have
As x approaches infinity, the numerator approaches 0 and the denominator approaches infinity, so the whole limit approaches 0. Therefore our original limit can be found because
Now, this was just the exponent of e in the definition of our original limit. Thus:
So we reach the conclusion that, as grows faster than