Ask Me Help Desk

Ask Me Help Desk (https://www.askmehelpdesk.com/forum.php)
-   Mathematics (https://www.askmehelpdesk.com/forumdisplay.php?f=199)
-   -   Limits at infinity (https://www.askmehelpdesk.com/showthread.php?t=617554)

  • Dec 6, 2011, 10:24 PM
    lato1
    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
  • Dec 7, 2011, 03:03 AM
    Aurora2000
    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

  • All times are GMT -7. The time now is 09:19 AM.