Sigmoid functions for the smooth approximation to $ \vert{x}\vert $

We present smooth approximations to $ \vert{x} \vert $ using sigmoid functions. In particular $ x\,erf(x/\mu) $ is proved to be better smooth approximation for $ \vert{x} \vert $ than $ x\,tanh(x/\mu) $ and $ \sqrt{x^2 + \mu} $ with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for error function.