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Homework Help: Value of this function as n approaches infinity

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data
    f(x) = lim [tex]_{n->\infty}[/tex](x[tex]{n}[/tex])/(1+x[tex]{n}[/tex])

    2. Relevant equations

    Suppose that x=1

    3. The attempt at a solution

    Wouldnt f(x) = 1/2? Because 1^n = 1, so the denominator is 2. The solution says that f(x)=1. Why is that?
  2. jcsd
  3. Feb 14, 2010 #2
    yes the answer is f(x)=1 because both of them have the highest power of n so based on that if you have the same power you just take the cofficient which is one.
    x^n/x^n = 1 when the limit goes to infinity.
  4. Feb 14, 2010 #3


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    Gold Member

    Yes f(1) is 1/2. The limit is 1 if x > 1 and 0 for x between 0 and 1.
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