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Help me find this limit!

  1. Nov 2, 2011 #1
    I can't seem to figure out how to find this seemingly simple limit (that is shown numerically to go to 0)

    lim x → ∞ ( x rx )

    for r < 1

    This is an indeterminate form of ∞ * 0, but when I try to apply L'Hôpital's rule as

    lim x → ∞ ( rx / ( 1 / x ) )

    I end up getting an expression of the form x2 rx, with further application of the rule generating higher and higher powers of x

    I'm totally stuck!
     
  2. jcsd
  3. Nov 2, 2011 #2

    gb7nash

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    Homework Helper

    You have the right idea. Try this instead:

    lim x → ∞ (x/(1/r)x)
     
  4. Nov 3, 2011 #3
    But wouldn't that be ∞ / ∞ ? L'Hopital's rule only applies to 0 / 0
     
  5. Nov 3, 2011 #4

    gb7nash

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    Homework Helper

    No it doesn't. It also applies to +- inf/inf
     
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