Revisiting real functions with constant limit at infinity. What about the limit of their derivative there?

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Dated: 12 September 2021

Actually, the discussion about whether for a real function f(x) having a constant limit as x approaches infinity the limit of its derivative f'(x) as x approaches infinity must be zero was over for me almost five years ago with the definite conclusion that the answer is no. Recently, Itzhak Barkana claimed that the answer was yes, after all, and wrote a paper, to which you can find a link in the pdf file below. In addition, the file contains an essay demonstrating (among other things) that Barkana is wrong. The answer no remains correct for the general case. A simple criterion is given the addition of which makes the limit of f'(x) definite (this criterion is existence of lim_x→∞ f’(x)), and it is shown that in this case it must be zero indeed. Barkana's ideas can be used to define f'(∞), but then the function f'(x) will be discontinuous at infinity for the counterexamples presented before. Thus, these counterexamples prevail.

Revisiting real functions having a constant limit as x→∞. What can we say about the limiting behavior of their derivative? 12.09.2021

Next: Sagnac effect   Up: Introduction science education project    Previous: About Bohmian mechanics

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