Powers Drown Logarithms/Corollary

Theorem

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

Then:

$\ds \lim_{y \mathop \to 0_+} y^r \ln y = 0$

Proof

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

$\blacksquare$

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 14.3 \ (2) \ \text{(ii)}$