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Find the limit of x^2(√(x^4+5)-x^2) as x->∞

  1. Nov 15, 2011 #1
    Find the limit of x^2(√(x^4+5)-x^2) as x->∞. I think it might be a L'Hospitals rule, but I'm not sure. We haven't done many problems like this yet, thanks!
  2. jcsd
  3. Nov 15, 2011 #2


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    L'Hospital's Rule is valid only for certain indeterminate forms, like infinity/infinity or 0/0.
    You should be able to determine this limit by inspection.
  4. Nov 15, 2011 #3


    Staff: Mentor

    Right. L'Hopital's Rule is not applicable here.
    I don't know about that. This limit is another of the indeterminate forms - [∞ * 0].

    I would multiply the expression in the limit by 1, in the form of [itex]\sqrt{x^4 + 5} + x^2[/itex] over itself.
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