Powers Drown Logarithms/Corollary

Theorem
Let $r \in \R_{>0}$ be a (strictly) positive real number.

Then:
 * $\displaystyle \lim_{y \mathop \to 0_+} y^r \ln y = 0$

Proof
Put $y = \dfrac 1 x$ in the Powers Drown Logarithms.