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Homework Help: Pointwise convergence of (x^n)/(1 + x^n)

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the function that (x^n)/(1 + x^n) converges to as n goes to infinity, on the interval [0,2]


    2. Relevant equations



    3. The attempt at a solution
    I've worked out the fact that on the interval [0,1) it converges to 0, and when x is 1 it converges to 1/2, but for the life of me I'm not sure what the first step of proving what it converges to on the (1,2] interval. hints?
     
  2. jcsd
  3. Dec 1, 2011 #2

    Dick

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    Divide numerator and denominator by x^n. Now can you figure out what it converges to on (1,2]?
     
  4. Dec 1, 2011 #3
    Yes! It becomes 1 / ( 1/(x^n) + 1), which goes to 1 / (0+1) = 1.

    Thank you so much :)
     
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