Question

Question #4e666

Answer 1

`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`