Powers Drown Logarithms/Corollary

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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