Saturday, 23 January 2016

calculus - Computing limlimitsxtoinftyln(x)cdotln(1ex)

Limit as x approaches infinity of ln(x)ln(1ex):
lim



The only thing I can think to do is rewrite the ln(x) on the bottom as (lnx)^{-1} and use L’Hôpital’s rule, but I’ve done two iterations now and it keeps getting back to the 0/0 or infinity*0 indeterminate case. Any help on how to proceed will be much appreciated! Thanks

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