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Limits of log

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data
    I want to find the limit as n approaches infinity of (n^n)*(x^(n^2)), and

    2. Relevant equations
    My teacher told us to look at the log. 0<x<1. Also, since the log of this goes to -infinity, then the original limit in question goes to 0.

    (1) why is looking at log valid, if log is only defined for positive numbers
    (2) how did we figure out that the limit goes to 0 by looking at the log function?
  2. jcsd
  3. Feb 10, 2010 #2


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    (1) if 0<x<1 what's not positive here? (2) if you can show that the log of that quantity goes to -infinity, then you will have shown the original quantity goes to zero. Numbers whose logs are huge negative numbers are positive numbers close to zero. Listen to your teacher.
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