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Limit of [1 + sin(x)]^(1/x) when x approaches 0

  1. Apr 5, 2008 #1
    Can somebody solve this problem: the limit of [1 + sin(x)]^(1/x) when x approaches 0 ?
     
  2. jcsd
  3. Apr 5, 2008 #2
    Take the logarithm of that expression, which will let you use L'Hopital to solve it.
     
  4. Apr 6, 2008 #3

    arildno

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    The simplest is to rewrite this as:
    [tex](1+\sin(x))^{\frac{1}{x}}=((1+\sin(x))^{\frac{1}{\sin(x)}})^{\frac{\sin(x)}{x}}[/tex]
    The correct limit is quite easy to deduce from this.
     
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