Limit of x to the x

Theorem
Let $f: \R \to \R$ be defined on $\closedint 0 \to$ with $\map f x = x^x$.

Then:
 * $\ds \lim_{x \mathop \to 0^+} x^x = 1$

Equivalently, from the definition of power:
 * $\ds \lim_{x \mathop \to 0^+} \map \exp {x \ln x} = 1$