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Math Help - limit refresher

  1. #1
    Member pberardi's Avatar
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    limit refresher

    Could some please explain how to take this limit?

    lim x ->2/3 1/(3x-2)^3

    and a similar one

    lim x ->2/3 7/(3x-2)^2

    Thanks,
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  2. #2
    MHF Contributor Calculus26's Avatar
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    lim x ->2/3 1/(3x-2)^3 yields 1/0 so the limit could be inf,-inf or DNE

    So consider onesided limits

    lim x ->2/3+ ( 1/(3x-2)^3) = infinity since if x > 2/3 3x-2 > 0 and
    (3x-2)^3 > 0

    lim x ->2/3- (1/(3x-2)^3) = neg infinity since if x < 2/3 3x-2 < 0 and

    (3x-2)^3 < 0

    Therefore lim x ->2/3 1/(3x-2)^3 DNE

    Note if we had (3x-2)^2 then both limits would be infinity and the limit would be infinity
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  3. #3
    Member pberardi's Avatar
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    And the second one is infinity from both sides so the limit is positive infinity correct?
    Ooops just saw the last line of your post. Thanks.
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  4. #4
    MHF Contributor Calculus26's Avatar
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    you got it--
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