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Math Help - Continuous functions and boundedness

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    Continuous functions and boundedness

    Let be f : [a,inf)-->R is is continuous function and suppose that { limf(x) x-->inf } exist.Prove that f is boundedon [a,inf) so f is bounded function.
    Last edited by mr fantastic; January 3rd 2010 at 10:04 PM. Reason: Changed post title
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    Since the limit exists (say it's L) there is an integer M such that if x>M we get \vert f(x)-L \vert <1 and using the triangle inequality we get \vert f(x) \vert < 1+\vert L \vert. Now consider f:[a,M] \rightarrow \mathbb{R} since it's cont. on a compact set so it attains a maximum and a minimum (say A,B resp ) then \vert f(x) \vert < \max \{ 1+\vert L \vert ,\vert A\vert ,\vert B \vert \} on [a, \infty )
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