Question

As x approaches 1 from the right side, what's is the limit of ln(ln(x))? Is it - inifity?

Answer 1

-inf looks correct. The lnx approaches 0 as x approaches 1 from the right, and the outer function ln(lnx) approaches -inf as lnx approaches 0.

Answer 2

Since the limit of lnx exists as x approaches 1, you can treat that internal limit separately first. That turns the problem into "as x approaches 1 for ln(ln(x))" to "as x approaches 0 for ln(x)," which diverges to -infinity.

Answer 3

A graph will confirm: https://www.google.com/search?q=ln(ln(x))&oq=ln(ln(x))&aqs=chrome.0.69i57j0l3j69i62l2.3769j0&sourceid=chrome&ie=UTF-8

Look at where the function approaches as you approach 1.