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Math Help - Urgent!!

  1. #1
    Junior Member miss_lolitta's Avatar
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    Angry Urgent!!

    can someone help me to prove that:


    if y(t)> 0 and increasing function then:

    y(t) tends to infinite as t tends to infinite ??!


    thanks in advance,,
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  2. #2
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    Quote Originally Posted by miss_lolitta View Post
    can someone help me to prove that:
    if y(t)> 0 and increasing function then:
    y(t) tends to infinite as t tends to infinite ??!
    Of course, the proposition is false.

    Consider y(t)=arctan(t)+pi/2.
    The function y is certainly positive and increasing.
    If fact it is a very, very well behaved function.
    But the function y is bounded above by pi.
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  3. #3
    TD!
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    I deleted my stupid reply, amazing how one can be deceived by a false statement
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  4. #4
    Junior Member miss_lolitta's Avatar
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    just!!i wona to tell u that :

    y(t) is not a bounded


    thans for all
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  5. #5
    TD!
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    Now that makes more sense and it would've made my "proof" valid.

    So we have y(t) > 0, increasing and unbounded. For the function not to diverge (go to infinity), it would have to converge to a real value or oscillate. It cannot oscillate since it's increasing, y(b) > y(a) for every b > a. It can't converge to a real value (say L) either, since that would make it bounded (by L).
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