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L'Hospital's Rule (products)

  1. Oct 27, 2011 #1
    I came across the problem lim as x approaches infinity of xln((x+3)/(x)). This is an indeterminate limit so L'Hospitals rule must be used to evaluate it. I solved it to come out to negative infinity, but the graph says it's three. What did I do wrong in solving it?
  2. jcsd
  3. Oct 27, 2011 #2
    Can I see what you've done?
  4. Oct 27, 2011 #3


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    Homework Helper

    x log((x+3)/x)=3 [log(1+3/x)-log(1)]/(3/x)
    then you won't need L'Hospital's Rule which would work despite being unneeded. As far as what the mistake was how would anyone know?
  5. Oct 27, 2011 #4


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    Science Advisor

    You can also use the power series for ln: ln(1 + 3/x) = 3/x +O(1/x2)
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