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Limit question !

  1. Jan 6, 2012 #1
    1. The problem statement, all variables and given/known data

    I know it needs L'Hopital but i can't get it to the indeterminant form

    Limit (x-(x+2)e^(1/x)) ((inf - inf ))

    I reached until here and then i got stuck

    (1-((x+2)e^(1/x))/x)/(1/x) (1 -inf/inf)/0
  2. jcsd
  3. Jan 6, 2012 #2


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    Separate limit into [itex]\lim_{x \rightarrow \infty} x(1 - e^{\frac{1}{x}}) - 2e^{\frac{1}{x}}[/itex].

    Second term is easy.

    First term is indeterminate of the form infinity*0, so reexpress it as [itex]\frac{1 - e^\frac{1}{x}}{\frac{1}{x}}[/itex], then let [itex]y = \frac{1}{x}[/itex] and take the limit as [itex]y \rightarrow 0[/itex] using L' Hopital's Rule.
  4. Jan 6, 2012 #3
    Oh i see :D !! Thanks alot :)
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