Given a function $f(x)$ does there exist a sequence of smooth functions that $f_{n}(x) \to f(x)$ as $n \to 0$?
I am currently trying to smooth out a kink for the general function $x^{1/p}$.
An example of what I mean: $$f(x) = |x| \qquad f_n(x) = (x^{2}+n)^{1/2}$$