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Simple Limit

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    lim x->0 ( (a^x - 1)/x )

    2. Relevant equations

    NA

    3. The attempt at a solution

    The professor told me that the answer to that limit is log(a), but why? I don't understand; can someone explain why?
     
  2. jcsd
  3. Oct 10, 2011 #2

    gb7nash

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    Do you know l'hopital's rule?
     
  4. Oct 10, 2011 #3

    Yeah, I just figured it out. Take the derivative of both the numerator and the denominator and then it's easy from there...

    Is there any way to do it without having to use L'Hospital's?
     
  5. Oct 10, 2011 #4

    gb7nash

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    You could take the maclaurin series of a^x and plug it in for a^x. Once you do this, stuff cancels out and you'll obtain the same answer.
     
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