L'hopitals rule?

  • Thread starter kmeado07
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  • #1
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Homework Statement



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

Homework Equations





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?
 

Answers and Replies

  • #2
MathematicalPhysicist
Gold Member
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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?
 
  • #3
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yea, thank you!
 

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