How do you find the limit $lim x^-x$ as $x->oo$ ?

Question

1489 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-01T10:17:52

$= 0$

$lim_(x to oo) x^(-x)$

$= lim_(x to oo) exp(ln x^(-x) )$

$= lim_(x to oo) exp(- xln x )$

$= lim_(x to oo) exp( - lim_(x to oo) x * lim_(x to oo) ln x )$

$= 0$

How do you find the limit lim x^-xlim x^-x as x->oox->oo?