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Homework Help: Limits of x/ln(x)

  1. May 19, 2015 #1
    1. The problem statement, all variables and given/known data
    Hello all,

    I am having hard time with limits.

    1. limx->1- x/ln(x)

    2. limx->1+ x/ln(x)
    2. Relevant equations

    3. The attempt at a solution
    1. limx->1- x/ln(x)
    = 1-/ln(1-)
    ln(1-) = 0-

    I seriously dont understand why ln(1-) = 0-

    2. limx->1+ x/ln(x)
    = 1+/ln(1+)
    ln(1+) = 0+

    I seriously dont understand why ln(1+) = 0+

  2. jcsd
  3. May 19, 2015 #2
    Do you know what the natural logarithm graph looks like?
  4. May 19, 2015 #3
    yes I do, doing limits with a graph is easy, I have to resolve this by doing algebra.
  5. May 19, 2015 #4
    You say you don't understand why ln(1) = 0. This is common knowledge about the logarithmic function. You have a function approaching 0 in the denominator and a function approaching 1 in the numerator. What does that tell you?
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