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Lim x->0+ (x^cos(1/x))

  1. May 6, 2017 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations


    3. The attempt at a solution
    let y = lim x->0+ x^cos(1/x)
    lny = cos(1/x)*lnx = (x*cos(1/x)) * (lnx/x)

    x*cos(1/x) = 0 (sandwich theorem)
    lnx/x = 0 (l'hopital)
    so lny = 0
    and y = 1
    Is this correct?
     
  2. jcsd
  3. May 6, 2017 #2

    PeroK

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    No, that doesn't look right at all.

    what happens when ##\cos(1/x)## is negative?
     
  4. May 6, 2017 #3
    Well then y would tend to infinity but the limit is x-> 0+
     
  5. May 6, 2017 #4

    Ray Vickson

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    He is not asking about what happens to x; he is asking about what happens to x^cos(1/x).
     
  6. May 6, 2017 #5
    tends to infinity I guess
     
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