Question

How do you find the limit of `ln(ln(x))/x` as x approaches `oo`?

Answer 1

0

Explanation:

`lim_(x->oo) ln(lnx)/x =ln(ln oo)/oo = ln oo/oo =oo/oo`

This is an indeterminate type so we can use l'Hopital's Rule. Therefore, find the derivative of the top and the derivative of the bottom and then find the limit of their quotient as x goes to infinity.
i.e
`lim_(x->oo) (f'(x))/(g'(x))`

`lim_(x->oo) (1/lnx * 1/x)/1 = lim_(x->oo)1/(xlnx)`

`=1/oo = 0`