Question

What is the limit of `ln(ln(x))/x` as x approaches `oo`?

Answer 1

`0`

Explanation:

simply because `x` outgrows `ln x` we know that this is going to be zero, but as it is in `oo/oo` indeterminate form, we can use L'Hopital's rule

`lim_(x to oo) ln(ln(x))/x`

`= lim_(x to oo)( 1/ln(x)* 1/x) /1`

and the limit of the product is the product of the limits
`= lim_(x to oo) 1/ln(x)* lim_(x to oo) 1/x = 0`