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Homework Help: L'hopitals rule?

  1. Jan 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the limit of f(x)=[xcosx]/[x^3 + 1] as x tends to infinity.

    2. Relevant equations



    3. The attempt at a solution

    Can i use l'hopitals rule here? Or if not, what are the conditions for f(x) to meet so that i may use l'hopitals rule?

    Without using l'hop i know that cosx would oscillate between -1 and 1 and that is multiplied by infinity. Then the denominator would tend towards infinity. So what is infinity over infinity?
     
  2. jcsd
  3. Jan 24, 2009 #2

    MathematicalPhysicist

    User Avatar
    Gold Member

    I think that you don't need L'hopital here.
    i.e, if we write it as:
    (cos(x)/x^2)*1/(1+1/x^3)->0
    as x appraoches infinity, can you see why?
     
  4. Jan 24, 2009 #3
    yea, thank you!
     
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