While investigating the problem of finding the ratio between radius and height that provides the minimum surface area for a fixed volume, I made a mistake and ended up with what turned out to be an usual function. Stripped of such extraneous constants, this is the function that I discovered:
The unusual behaviour that it has is that it is discontinuous and undefined at x=0 and yet it has limits of 1 and -1 respectively as x --> 0 from the positive and negative directions. Here is what WolframAlpha turned up:
Furthermore, my mobile version of WolframAlpha shows the step-by-step solutions to the derivation of the limit:
So there we have it and I obviously have to brush up on l'Hôpital's rule which I certainly remember from the old days but the details completely elude me now.
