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Homework Help: Positive integers for k: finding limits

  1. Sep 24, 2011 #1
    1. The problem statement, all variables and given/known data
    find the positive integers k for which

    lim x->0 sin(sin(x))/x^k


    2. Relevant equations

    exists, and then find the value of the limit

    3. The attempt at a solution
    I did the first three k's

    k=0
    lim x->0 sin(sin x))/x^0= 0 undefined

    k=1
    lim x->0 sin(sinx))/x^1= 1

    k=2 I might be wrong with this
    lim x->0 sin(sinx))/x^2= undefined

    k>2 how do I do this one.
    lim x-> sin(sinx))/x^k>2=?
     
  2. jcsd
  3. Sep 24, 2011 #2

    SammyS

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    0 is not positive.

    Regarding k = 2: How did you arrive at your answer for k = 1 ??
     
  4. Sep 24, 2011 #3
    well I plugged it into my calculator
     
  5. Sep 24, 2011 #4
    What happens if you multiply and divide sin(x)?
     
  6. Sep 24, 2011 #5
    I'm not sure.
     
  7. Sep 24, 2011 #6
    Do it an see what you recognize
     
  8. Sep 24, 2011 #7
    well in the table for k=2

    it goes from -100 then an error then 99

    so it must be for all positive numbers and above should be infinity?
     
  9. Sep 24, 2011 #8

    SammyS

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    Are you saying that your calculator says that sin(sin(0))/0 = 1 ?
     
  10. Sep 24, 2011 #9
    I used a different method.. but that answer sin(sin(0))/0 does not exist right
     
  11. Sep 24, 2011 #10

    SammyS

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    Right.

    So, I ask again. How did you find the answer when k = 1 ?
     
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