Thursday, 23 October 2014

calculus - Function whose integral over [0,infty) is finite, but the limit of the function is >0

Let tR,f:RR:tf(t).




f is required to have:




  1. lim, where L>0 (could be \infty, so the limit exists, only it could be \infty)


  2. \displaystyle\int_{0}^{\infty} f(t) dt < \infty




Is that possible to construct such f?



Note:




f can be any function continuous or discontinuous.



I found the discussion here which is involving "tent" function but in that example, the limit does not exist.



Note 2: I have edited the title. Thank you for your fedback !!!



Thank you for any answers or comments.

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