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Homework Help: Compute the limit (exponents with variable)

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data
    Compute the limits of the following sequence (show your work):


    (sorry if it looks funny ... the top line is divided by the bottom line)

    3. The attempt at a solution
    I was thinking that I should get the exponents the same and add/subtract the exponents, but I don't remember how to, or if this is even possible.
  2. jcsd
  3. Nov 2, 2011 #2
    I think I figured out a bit more. I have learned that I can split up the limit, so it will look like:
    (lim3n+1)(lim7n+3) ÷ (lim4n)(lim5n-2)

    and each of these individual limits equals +∞.

    So I have +∞ ÷ +∞. Does this still equal infinity, 0, or does not exist?
  4. Nov 2, 2011 #3


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    Science Advisor
    Homework Helper

    Try this. 2^n/3^n=(2/3)^n. What's the limit of that? How about 3^n/2^n? There's a reason why infinity/infinity is called 'indeterminant'.
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