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Limit of y=((x-1)/x)^x as x approaches inf

  1. Aug 24, 2009 #1
    I reasoned that (x-1)/x is always less than 1 for positive x. Therefore it will tend to zero as the exponent tends to infinity. But what is confusing is that when working it out for 1 to 100, the value increases.

    Is the the limit 0?, and when does the limit "turn".
    Last edited: Aug 24, 2009
  2. jcsd
  3. Aug 24, 2009 #2


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    The limit is not 0. Use [itex]\lim_{x \to 0} (1+x)^{\frac{1}{x}}=e[/itex].
  4. Aug 25, 2009 #3
    alternatively you can take the natural log of both sides,

    ln y = x ln ((x-1)/x) = ln((x-1)/x)/(1/x)

    then apply l'hopital's rule to get a nice simple solution, don't forget to then exponent it to solve for y! :)
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