Wednesday, 29 November 2017

calculus - Prove that limlimitsxtoinftyefracln(x)x=1



How to prove that lim?



I know that x grows much faster to infinity then \ln(x), therefore the limit equivalent to e^0 = 1



but that's not a rigorous proof.



Answer



\lim_{x \to \infty}\frac{\ln{x}}{x}=\lim_{x \to \infty}\frac{1}{x}=0



by L Hopital's Rule


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