L'Hospital's Rule (products)

  • Thread starter SpockTock
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  • #1
SpockTock
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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?
 

Answers and Replies

  • #2
dacruick
1,042
1
Can I see what you've done?
 
  • #3
lurflurf
Homework Helper
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write
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?
 
  • #4
mathman
Science Advisor
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550
You can also use the power series for ln: ln(1 + 3/x) = 3/x +O(1/x2)
 

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