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Need help evaulating a few limits

  1. Feb 29, 2012 #1
    I made up this limit problems trying to understand something in chemistry, so they may not necessarily have any answer.

    I am not sure how to evaluate them analytically. Not sure how L'Hopital's Rule would work here either.

    [tex] (\lim_{V→50^{-}}-log(\frac{50-V}{10(V+50)})) [/tex]

    [tex] 14+(\lim_{V→50^{+}}log(\frac{V-50}{10(V+50)})) [/tex]

    [tex] 14+(\lim_{V→∞}log(\frac{V-50}{10(V+50)})) [/tex]

    I would greatly appreciate all your help on these questions!

    Just in case anyone asks, I am trying to model the pH of a solution as a function of the volume of titrant added, but I want to make sure it is piece-wise continuous.

    Thanks!

    BiP
     
  2. jcsd
  3. Mar 1, 2012 #2

    HallsofIvy

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    log(x) is continuous for x> 0 so [itex]\lim_{V\to 50^-} log((50- V)/(10(V+ 50))= log(\lim_{V\to 50^-} (50-V)/(10(50+ V))[/itex]

    And since the denominator does not go to 0 as V goes to 50, you cannot use "L'Hopital's rule" nor do you need to. As V goes to 50, from below, the numerator goes to 0 while the denominator goes to 1000 so the argument of log goes to 0 and so the limit is [itex]-\infty[/itex].
     
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