Question

How do you find the limit of `(ln (ln (x) ) ) / ( ln (x) )` as x approaches `1`?

Answer 1

`+-oo`

Explanation:

Use limit `f(x)/g(x)` = limit`( f'(x))/(g'(x))`.

As `xto1, (ln(ln(x)))/(ln(x))to lim ((ln(ln(x)))')/((ln(x))')`

`= lim ((1/(ln x))(1/x))/(1/x)= lim 1/(ln x)=1/0=+-oo`

Note that the left and the right limits of 1/ln x, as `xto1, are +-oo`. .