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Homework Help: I can't seem to find this limit

  1. Jan 9, 2016 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations

    3. The attempt at a solution
    I tried using the rule of multiplying with the "conjugate", for example what's above multiplied by (√n^3+3n)+(√n^3+2n^2+3)/(√n^3+3n)+(√n^3+2n^2+3).
    But I'm left with a huge mess :(
    I also tried dividing the top and the bottom by n^2 in the square roots to get the n out, but that didn't work either :(
  2. jcsd
  3. Jan 9, 2016 #2


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    The conjugate method looks good here. It doesn't give a mess in the numerator, right? In the denominator, do you need all the terms, or is it sufficient then only to look at the leading terms?
  4. Jan 9, 2016 #3
    The image is so bad I can't even see the value of the exponents, try to write it out in latex next time.
    Assuming what you wrote is ##\frac{\sqrt{n^3+3n}-\sqrt{n^3+2n^2+3}}{\sqrt{n+2}}##
    multiplying with the conjugate works for me. After you done that note that only the "highest order" terms matter.
  5. Jan 10, 2016 #4


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    After you multiply by the conjugate, you want to pull the highest power of n, not ##n^2##, out of each of the square roots.
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