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Finding the Limit by Interpreting an Expression as an Appropriate Derivative

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Find Lim [ 1/h*ln(3+h)/(3)] by interpreting the expression as an appropriate derivative.
    h→0

    2. Relevant equations

    I am confused on how to solve this problem for a review packet for Calc BC. I seem to have forgotten how to solve this problem and hopefully someone can give me some pointers!
     
  2. jcsd
  3. Nov 19, 2009 #2

    Mark44

    Staff: Mentor

    Are you sure you have the problem written correctly? Something like this, maybe?
    [tex]\lim_{h \rightarrow 0}\frac{ln(3 + h) - ln(3)}{h}[/tex]

    What you have doesn't look like a limit expression for any derivative that I can think of.
     
  4. Nov 20, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The second "3" should be inside the logarithm: ln((3+h)/3)= ln(3+h)- ln(3)

    (1/h) ln((3+h)/3)= (1/h)(ln(3+h)- ln(3)) is the difference quotient for the derivative of ln(x) at x= 3.
     
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