Calc limits --> L'hopital's rule?

Question

please help me... I need to find the limit (as x --> 0+) of ln (x) / x; using L'hopital's rule if possible. However, as L'Hopital's rule requires a 0/0 or inf/inf solution and for the limits to be differentiable, and i'm coming up w/ -inf/0 as the original limit...I'm lost.

Thanks for any help you can offer me.

Answer 1

You are correct - this is -∞/0, which is a determinate form - this function always diverges. Therefore, if the limit exists, it must be ±∞. Since the function is always negative as you approach 0 from the right, [x→0+]lim ln x/x = -∞. The use of L'hopital's rule is neither possible nor required.