From: "Jonathan W. Hoyle" Subject: The function f(x) = e^-e^-1/x Date: Wed, 17 Mar 1999 03:06:03 -0500 Newsgroups: sci.math Keywords: Example of discontinous limits Notice that the function f(x) = e^-e^-1/x is defined for all x not 0, and lim x->0+ f(x) = 1, yet lim x->0- f(x) = 0. Also, 0 < f(x) < 1 for all nonzero x, and it is even one-to-one. Such a discontinuity seems strange for such a smooth bounded function, with derivatives of all orders on R - {0}. Can you come up with other smooth bounded functions written in closed form such that lim x->0- f(x) and lim x->0+ f(x) both exist and are different? The goal is to use a single closed form equation, avoiding things like f(x) = x if x<0, x+1 if x>0.