Edit: Apparently Mother Nature is being a bit senile today. The weather has been rain, ice, rain, snow, and now rain again. If the temperature drops, the commute tomorrow will be made of pure, unadulterated suck.
Great Caesar's Ghost! I can't wait for tomorrow.
I'm looking for families of functions with specific properties: A horizontal asymptote at positive infinity and a first derivative that is always positive. So far I've found three families:
The Sigmoid functions — arctan, erf, &c. Two asymptotes, continuous.
Polynomials of the form x^-(2n+1). Two asymptotes, singularity at x=0.
Exponential functions of the form -a^-x. One asymptote, continuous.
If anyone can think of additional families, I'd appreciate it.
Repo Man (1984)
J. Frank Parnell: Ever been to Utah? Ra-di-a-tion. Yes, indeed. You hear the most outrageous lies about it. Half-baked goggle-box do-gooders telling everybody it's bad for you. Pernicious nonsense. Everybody could stand a hundred chest X-rays a year. They ought to have them, too. When they canceled the project it almost did me in. One day my mind was full to bursting. The next day - nothing. Swept away. But I'll show them. I had a lobotomy in the end.
Otto: Lobotomy? Isn't that for loonies?
Parnell: Not at all. Friend of mine had one. Designer of the neutron bomb. You ever hear of the neutron bomb? Destroys people - leaves buildings standing. Fits in a suitcase. It's so small, no one knows it's there until - BLAMMO. Eyes melt, skin explodes, everybody dead. So immoral, working on the thing can drive you mad. That's what happened to this friend of mine. So he had a lobotomy. Now he's well again.
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