## Friday, November 27, 2015

1. Properties of the function $x^x$ (Post-Doc Ergo Propter Hoc H/T Dave Richeson). Can you prove:
$\int_{0}^{1} x^{x} = -\sum_{n=1}^{\infty} (-n)^{-n}$
A strange derivative: let $f(x)=x^2 \sin(1/x^2)$ for $x \ne 0$, and $f(0)=0$. This function has $f'(0)=0$ even though $\lim_{x \rightarrow 0} f'(x),$ does not exist.