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Limits splitting the fraction into two

  1. Oct 23, 2003 #1
    I can't figure this one out. I've tried everything. I tried splitting the fraction into two, applying a log to each side, factoring the top, dividing by x2n, and Lhopitals rule doesn't apply and wouldn't help if it did. Any ideas?
    Last edited by a moderator: Feb 6, 2013
  2. jcsd
  3. Oct 23, 2003 #2
    perhaps the only way to do this would be to consider various cases such as x>1, x=1, x<-1, x=-1, etc.
    anyone agree?

    I get for x>1
    for x=1, lim=0
    if 0<x<1, lim=-1

    What about x<0? What is -2^999999.5? Surely, it's not real. Can we say that lim DNE for x<0?
    For -1<x<0 x^n would be very small, but wouldn't n have to be some integer?
    Last edited: Oct 23, 2003
  4. Oct 23, 2003 #3
    I got stuck.

    For example,
    I'll omit the subscripts.

    As n grows to infinity, we can say nothing about the limit, because it depends on what x is. If x is small then 1/x is large. If x is big, then 1/x is small.

    edit: whoops edited wrong post, sorry.
    Last edited by a moderator: Oct 23, 2003
  5. Oct 23, 2003 #4


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    Grargh, you read and responded before I could delete my post.

    Yes, breaking it up into cases is a good idea.

    edit: n often implicitly means an integer, and it wouldn't surprise me if this problem assumed as such.

    *sigh* Today isn't my best day. :wink:
    Last edited: Oct 23, 2003
  6. Oct 24, 2003 #5


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    I would interpret this as n being an integer so you don't have any problems with fractional powers of negative numbers.

    Because x2n= (x2)n) it doesn't matter whether x is positive or negative so you might as well assume positive. In that case the crucial cases are: 0<= x<1, x= 1, x> 1.
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