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    lato1's Avatar
    lato1 Posts: 6, Reputation: 1
    New Member
     
    #1

    Dec 6, 2011, 10:24 PM
    limits at infinity
    I have 3 very tricky limits questions


    1 lim (x sin(x^2 e^x))/(x^2 1) as x approaches infinity.

    2 lim(1/(e^x sin(1/x^2)) as x approaches infinity

    3 lim(x-x^1/2 lnx) as x approaches infinity
    Aurora2000's Avatar
    Aurora2000 Posts: 111, Reputation: 16
    Junior Member
     
    #2

    Dec 7, 2011, 03:03 AM
    You can try use de l'Hopital rule when dealing with limits of form :

    1.
    Notice that , thus

    thus


    2.
    This is more tricky, you have to see who wins between (who goes to infinity) and
    (who goes to 0). Using

    you can have

    thus


    3. lim(x-x^1/2 lnx) as x approaches infinity
    It does not display correctly (maybe a plus sign is missing), but both

    and

    converge to infinity.
    You can verify this by using

    or similarly

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