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When the limit exists find it

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data

    For the following function decide whether f(x) tends to a limit as x tends to infinity. When the limit exists find it.


    2. Relevant equations

    f(x)=[xsinx] / [x^2 +1]

    3. The attempt at a solution

    Im not really sure what method to use for this question.
     
  2. jcsd
  3. Jan 22, 2009 #2
    Re: Limits

    well sinx cycles from -1 to 1, to infinity and x tends to infinity. What happens to:

    [tex] x^2+1\;\lim_{x\rightarrow\infty}[/tex]
     
    Last edited: Jan 22, 2009
  4. Jan 22, 2009 #3
    Re: Limits

    x^2 + 1 tends to infinity as x tends to infinity. So infinity over infinity?
     
  5. Jan 22, 2009 #4
    Re: Limits

    Actually not exactly as sinx goes from -1 to 1 to the limit of infinity and x goes to infinity so it's between - 1 x infinity and 1 x infinity, infinitely as x approaches infinity. Hehe that makes sense. :smile:
     
    Last edited: Jan 22, 2009
  6. Jan 22, 2009 #5
    Re: Limits

    As to my methodology,

    [tex]
    \lim_{x\rightarrow\infty}\frac{xsinx}{x^2+1}[/tex]

    Taking [tex]x^2[/tex] common, we have the above equation as,
    [tex]\lim_{x\rightarrow\infty}\frac{x^2(\frac{sinx}{x})}{x^2(1+\frac{1}{x^2})}[/tex]

    Now, cancelling [tex]x^2[/tex] terms and also we know that [tex]\frac{1}{\infty}=~0[/tex],

    Thus, the function tends to?
    (It cant get easier than this.. c'mon..)
     
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