How to prove limx→∞x99ex=0?
I wasn't sure how to do this because both the top and the bottom limits independently turns out to be infinity!
Answer
After successively applying L'Hopital's rule 100 times, you get:
limx→∞x99ex=limx→∞99!ex=0
This is due to the fact that exponentials always grow faster than polynomials. ex will eventually overcome x99.
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