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Question #4e666

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Apr 25, 2017

#L = lim _(x->oo) (1/x)^lnx#

#ln L = lim _(x->oo) ln x cdot ln (1/x)#

#= lim _(x->oo) ln x cdot (ln 1 - ln x))#

#implies ln L = lim _(x->oo) - ln^2 x#

#implies L = lim _(x->oo) 1/e^( ln^2 x) #

# = 1/e^(lim _(x->oo) ln^2 x) = 0#

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