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One-sided limits

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    http://img831.imageshack.us/img831/8131/onesided.png [Broken]


    2. Relevant equations



    3. The attempt at a solution
    I am quite stumped on this problem. I don't think you can bring the limit inside the f(g(x)) function unless f(x) is continuous at the point about which the limit is being evaluated.
    That said, I'm quite unsure how to proceed. Any hints?

    Thanks.

    BiP
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 15, 2013 #2
    In each case, the nested function g(x) goes to zero as x goes to zero. So, you know the limit will be one of the two possibilities you're given. It's just a matter of figuring out which direction g(x) approaches zero from in each case. E.g. if g(x) is an odd function of x (with g(x) > 0 for small x > 0) with g(0)=0, then if x approaches zero from the left, which side does g(x) approach zero from? And if x approaches from the right? And so on.
     
    Last edited: Jan 15, 2013
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