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L'Hopital's Rule?

  1. Dec 9, 2013 #1
    (1)

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

    8xe^(1/x)-8x

    (2)

    L'Hopital's Rule

    (3)

    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

    Curious3141

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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

    ehild

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    [tex]\frac{1}{(\frac{1}{x})}[/tex]

    is the reciprocal of 1/x....

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

    FeDeX_LaTeX

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    Not quite.
     
  8. Dec 10, 2013 #7

    Curious3141

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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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