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About l'hopital rule

  1. Nov 29, 2007 #1
    [SOLVED] About l'hopital rule

    I have two solutions for a question about limit

    May I know is (a) correct, or (b)?
    What is the reason for the other to be wrong?

    (a) just directly applies l'hopital rule to numerator
    (b) is to reduce the numerator using logarithm formula before using l'hopital rule
  2. jcsd
  3. Nov 29, 2007 #2

    D H

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    You didn't calculate the derivative correctly for (b). You need to apply the chain rule. If you had computed it correctly you would have arrived at the same answer as for (a).

    [tex]\frac d{dx}(\ln(x+1)-\ln(2)) = \frac d {dx} \ln\left(\frac{x+1} 2\right) = \frac 2 {x+1} \; \frac d {dx}\frac {x+1} 2 = \frac 2 {x+1} \, \frac 1 2 = \frac 1 {x+1}[/tex]
  4. Nov 29, 2007 #3
    I see, thank you very much!
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