Trying to solve: \(\displaystyle\lim_{{{x}\to\infty}}{\frac{{{{\ln}^{{{1000}}}{x}}}}{{{x}^{{5}}}}}\)

Jakobe Norton 2022-04-10 Answered
Trying to solve:
limxln1000xx5
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Answers (1)

Terzago66cl
Answered 2022-04-11 Author has 8 answers
Be careful using limit operation.
First, let show that limx+lnxx=0. For t1, we have tt which imply for x1
0lnx=1xdtt1xdtt=2x22x
Then, for any a,b>0 and x>1, we have
lnbxxa=(lnxxab)b=(ba)b(ln(xab)xab)b
which answer your question.
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