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I have a function of this form $$f(t)=-k\cdot a(t)+l$$ where $a(t)$ is continously differentiable and $l$,$k$ are positive constants $a(t)$ satisfies the conditions

  1. $a(t)$ is defined from $[0,\infty)$ to $(0,\infty)$
  2. its integration is always less then plus infinity

What kind of conditions should I have on $l$, $k$ and $a(t)$ such that the the limit of the integration of $f(t)$ tends to minus infinity

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a(t)has a form like that using in noise attenuation – sabir Jan 12 '13 at 13:41
What do you mean with "its integration is always less than plus infinity"? As $a\colon [0,\infty)\to(0,\infty)$ is $C^1$, we clearly have $\int_0^x a(t)\,dt<\infty$ for all $x$. Do you mean that $\int_0^\infty a(t)\,dt<\infty$? – Hagen von Eitzen Jan 12 '13 at 14:02
so sorry, i wrote a mistake : i would like to say that the integration of a(t) between zero and infinity is infinity and the integration of a(t) square between zero and infinity is less than infinity – sabir Jan 13 '13 at 2:57

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