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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.

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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

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