Question

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

Answer 1

`= 0`

Explanation:

`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`