Find Limit of f(x) w/o L'Hopitals Rule

[kmeado07]

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?

 

[MathematicalPhysicist]

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?

 

[kmeado07]

yea, thank you!