what is lim as x approaches 1 for ln(ln x)/lnx ?
actually, the numerator only approaches $\displaystyle - \infty$ as $\displaystyle x \to 1$ from the right...
you are correct, but probably not for the reason you think you are. the problem is, as $\displaystyle x \to 1$ from the left, $\displaystyle \ln x$ is negative, and so $\displaystyle \ln ( \ln x )$ would be undefined. As the logarithm function is only defined when its argument is positive.
So since the numerator is undefined as we approach 1 from the left, the entire function is undefined there, and so the limit does not exist for that reason.
Now, $\displaystyle \lim_{x \to 1^+} \frac {\ln ( \ln x)}{\ln x}$ does exist. That should be fun for you to find (but not that difficult--honest)
I am not sure if this make sense. now I know that as x approchase 1 from the right ln(x)= negitive infinity.. so as x approchase to 1 from the right ln(ln(x))/ln(x)= ln(negitive infinity)/negitive infinity.. so now the numerator undifined and the denominator equal to negitive infinity
This all I know
um, yeah. i never thought of -1*1 though... i guess i thought, a negative number times a positive number gives a negative number, and a huge number times a huge number gives a huge number. and so, a huge negative number times a huge positive number will give a huge negative number. or something like that but yeah, your idea seems to work also