Logarithm Tends to Negative Infinity

Theorem
Let $x \in \R$ be a real number such that $x > 0$.

Let $\ln x$ be the natural logarithm of $x$.

Then:
 * $\ln x \to -\infty$ as $x \to 0^+$

Proof
From Derivative of Natural Logarithm Function $D \ln x = \dfrac 1 x$.

The result follows from Integral of Reciprocal is Divergent.