Question #4e666

1 Answer
Eddie
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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