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Finite limit problem

  1. Aug 28, 2012 #1
    1. The problem statement, all variables and given/known data

    I've read in my textbook, and confirmed via WolframAlpha that lim x->0 (cosx/x^0) =1 , and need an explanation for it. I thought it should be ∞ or something undefined, since 0^0 is undefined.

    2. Relevant equations



    3. The attempt at a solution

    I tried to use L'Hospitale on the expression, but that led to nowhere. There's no intermediate step between the expression and solution in both textbook, and Wolfram.
     
  2. jcsd
  3. Aug 28, 2012 #2

    Mark44

    Staff: Mentor

    Typo?
    There is no n in your limit expression.

    Is this the limit?
    $$\lim_{x \to 0} \frac{cos(x)}{x^0} $$
     
  4. Aug 28, 2012 #3
    It was a typo. Fixed, and yes that is the limit i was referring to!
     
  5. Aug 28, 2012 #4

    Mark44

    Staff: Mentor

    As long as x ≠ 0, x0 = 1, right? So, then, what is ##\lim_{x \to 0} x^0##?
     
  6. Aug 28, 2012 #5
    From all this my guess will be 1, but still not clear why. Is it because lim x->0 means that x !=0 but rather close to 0? Meaning some infinitesimal number ^0=1? Am i getting that correctly?
     
  7. Aug 28, 2012 #6

    Mark44

    Staff: Mentor

    Yes to both questions. The graph of y = x0 is a horizontal line with a hole at (0, 1).
     
  8. Aug 28, 2012 #7
    I understand now! Thank you very much for your help!
     
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