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Limits as n approaches infinity

  1. Jun 20, 2009 #1
    lim n-> infinity of:

    (n^4 + n^2 + 1)^0.5 - n^2 -1


    sin(2/n)/(1/n)


    (ln(n) + e^n)/(2^n + n^2)


    If anyone could explain the processes required to obtain the limits of any.. (or all) of these statements, that would be great
     
  2. jcsd
  3. Jun 20, 2009 #2

    zcd

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    In the first one, you could multiply the expression by its conjugate.

    For the second one, recall the identity lim t->0 sin(t) /t = 1. (substitute 2/n = t as t->0)

    For the third one, just apply l'hopital's rule several times.
     
  4. Jun 20, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Since this is your homework, try before you ask for help and then show what you have tried.
     
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