Limit of x to the x

Theorem
Let $f: \R \to \R$ be defined on $\left [{0 \,.\,.\, \to} \right)$ with $f \left({x}\right) = x^x$.

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

Equivalently, from the definition of power:
 * $\displaystyle \lim_{x \to 0^+} \exp \left({x \ln x}\right) = 1$