Alright, so I have been doing some stuff and I need to find a function in order to test my equations. I was using 1/x; however, this became difficult as it is infinite at 0. I would sinx/x however that is not strictly positive.

What I need is an always positive function with an asymptote at y=0, no vertical asymptotes and remains > 1 for a large number of units (5 to 10). Preferably 10. What I am attempting to study is an area cap phenomenon I have noticed with certain integrals involving the floor function and so I need a large function with which to experiment with.


closed as unclear what you're asking by The Great Duck, Dominik, John B, zhoraster, Henrik Dec 14 '16 at 16:35

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  • $\begingroup$ what about $(\sin x+2)/x$? $\endgroup$ – Crostul Nov 21 '15 at 8:59
  • $\begingroup$ I'm trying to avoid functions that cross the axes as that will introduce complications I would rather avoid at the moment. I wish to limit the number of variables I'm experimenting with. $\endgroup$ – The Great Duck Nov 21 '15 at 9:06
  • $\begingroup$ My function does not cross the axes. it's $(\sin (x) +2 )/x$ $\endgroup$ – Crostul Nov 21 '15 at 9:07
  • $\begingroup$ My mistake. I was thinking x + 2 was inside sin. Yes that is also one that appears useful. $\endgroup$ – The Great Duck Nov 21 '15 at 9:09

Try something like $$ \frac{a}{x^2+b^2} $$ for appropriate $a>0$ and $b$.


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