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-   -   Lim (cosx)^(1/x^2) x-->0 (https://www.askmehelpdesk.com/showthread.php?t=549674)

  • Jan 31, 2011, 08:55 AM
    susus
    lim (cosx)^(1/x^2) x-->0
    lim (cosx)^(1/x^2)
    x-->0
  • Jan 31, 2011, 09:42 AM
    ebaines

    Suggestion: if



    Then



    Now use de Moivre's theorem to find the limit of ln(L). Then L is e raised to that value.
  • Jan 31, 2011, 09:46 AM
    galactus

    A trick we can use is by observing that for



    Now, make the sub:

    and we get:



    Notice, this looks mighty similar to the famous 'e' limit:



    except we have a

    Thus, the limit is

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