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Homework Help: Struggling with this limit value.(probably using taylor series)

  1. Mar 1, 2014 #1
    Struggling with this limit value

    1. The problem statement, all variables and given/known data

    Calculate lim((e^x-1)/x)^(1/sin(x)) where x[itex]\rightarrow0[/itex]

    2. Relevant equations

    Maclaurin series.

    sin(x)/x -----> 1 when x->0 (possibly)

    3. The attempt at a solution

    (e^x-1)/x)^(1/sin(x) = ((x+x^2/2+x^3H(x))/x)^(1/sin(x)) =((1+x/2+x^2H(x))/x)^(1/sin(x))

    Then getting something like:

    1+(1/sinx)C(1)*(1+x/2+x^2H(x))/x) + (1+x/2+x^2H(x))/x)^2*(1/sinx)C(2)

    which results in total chaos.

    Anybody have a SIMPLE solution?

    p.s sorry for the lack of readability, writing math in Physicsforums is a F-ing pain. I mean what the H is [it0ex]\rightharp0oonup[/it0ex] and [itex0]\frac{}{0}[/itex0] telling me.
    Last edited: Mar 1, 2014
  2. jcsd
  3. Mar 1, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi Jarfi! :smile:
    log it first? :wink:
  4. Mar 1, 2014 #3
    ah, you genius you !
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