...satisfies the following conditions:(adsbygoogle = window.adsbygoogle || []).push({});

(1) Is continuous on [itex][1,\infty)[/itex], and

(2) Doesnothave a limit as [itex]x\to \infty[/itex].

Apparently, such a function [itex]f(x)[/itex] exists, but I cannot think of an example for the life of me. Remember: The function must also satisfy

[tex]

\int_1^\infty |f(x)|dx < \infty,

[/tex]

where "[itex]\int[/itex]" is the Lebesgue integral.

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# Can anyone come up with a Lebesgue-integrable function that

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