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Help! Prove Lim x-infinity cos(nx) = dne

  1. Nov 15, 2011 #1
    Help! Prove Lim x--infinity cos(nx) = dne

    Hey guys! I am new here however, I have been lurking around for a while. I need some help with a problem that I am currently working on. Here it is:

    1. The problem statement, all variables and given/known data

    Prove Lim x--infinity cos(nx) = does not exist


    3. The attempt at a solution

    As of now, I am not quite sure how to approach the problem. I know that I can say that if x is a multiple of 2π then it will converge to 1 however, if it is not a multiple of 2π then it will simply oscillate until infinity. As such, the limit does not exist. However, I doubt that that is what is required of the problem. I am thinking that there must be some systematic setup that I can use to prove this problem otherwise. Is there such a way or is my reasoning correct?

    In our other problems, we used epsilon-delta proofs to prove that certain functions converged to p.

    Anythings would help! Thanks guys!
     
  2. jcsd
  3. Nov 15, 2011 #2
    Re: Help! Prove Lim x--infinity cos(nx) = dne

    This reminds of a problem I had to do recently. Here are my thoughts:
    Pick 2 sequences (x[itex]_{n}[/itex])[itex]_{n}[/itex] and (y[itex]_{n}[/itex])[itex]_{n}[/itex] such that lim x[itex]_{n}[/itex] = infinity as n tends to infinity and lim y[itex]_{n}[/itex] = infinity as n tends to infinity. Then show that lim f(x[itex]_{n}[/itex]) ≠ lim f(y[itex]_{n}[/itex]), therefore the limit does not exist.
     
  4. Nov 15, 2011 #3
    Re: Help! Prove Lim x--infinity cos(nx) = dne

    So if I understand your statement correctly, I should choose for example cos(2πn) and show that that the limit goes to 1 and then pick any other to show that it goes to some other number? So basically my reasoning was right?
     
  5. Nov 15, 2011 #4
    Re: Help! Prove Lim x--infinity cos(nx) = dne

    Yes it is correct.
     
  6. Nov 15, 2011 #5
    Re: Help! Prove Lim x--infinity cos(nx) = dne

    got it thanks!
     
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