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Homework Help: L'Hopital's Rule?

  1. Dec 9, 2013 #1

    Evaluate the limit as x goes to infinity using L'Hospital's rule:



    L'Hopital's Rule


    How can I use L'Hopital's Rule for this problem if the denominator is 1? Wouldn't that just give me an undefined limit? This may be a pretty stupid question, but I'm new to this.
  2. jcsd
  3. Dec 9, 2013 #2


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    Hint: factorise first. Also, ##x = \displaystyle \frac{1}{\frac{1}{x}}##.
  4. Dec 10, 2013 #3
    How do you you know that x=(1)/(1/x)?
  5. Dec 10, 2013 #4


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    is the reciprocal of 1/x....

  6. Dec 10, 2013 #5
    Ahhh ok so I can rewrite as (8x(e^(1/x)-1))/(1/x)?
  7. Dec 10, 2013 #6


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    Gold Member

    Not quite.
  8. Dec 10, 2013 #7


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    That x is replaced by the 1/(1/x) term. So why does it appear again?

    Sorry no latex. On my phone at the moment.
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