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Limit x*sin(x) , x->inf

  1. Jun 22, 2009 #1
    1. The problem statement, all variables and given/known data
    The complete exercise is:

    If [itex]\lim_{x->\inf } \frac{f(x)-5x^2sin(x)}{(\sqrt (x^2+2))-x} = 7[/itex]

    show that [itex]\lim_{x->\inf} \frac{f(x)}{x} = 5[/itex]

    2. Relevant equations
    How do I show that [itex]\lim_{x->\inf} xsinx =1[/itex], because I run into it!

    3. The attempt at a solution

    I set K(x) = the fraction of the first limit and I solved for f(x) (x=0 excluded).

    Then I have the limit [itex]\lim_{x->\inf} \frac{f(x)}{x} = \lim_{x->\inf} K(x)*0 + 5 xsinx[/itex].

    Yet finally I reach the limit I spoke about in 2.
    Last edited: Jun 22, 2009
  2. jcsd
  3. Jun 22, 2009 #2


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    You can't, it eventually oscillates between +/- infinity. What exactly is f(x) in this context?
  4. Jun 22, 2009 #3
    Random function. It doesn't specify... Any other solutions?
  5. Jun 22, 2009 #4


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    Maybe you're omitting part of the question?
    If [itex]
    \lim_{x->\inf } \frac{f(x)-5x^2sin(x)}{(\sqrt (x^2+2))-x}
    doesn't say anything because you're only giving the condition. Does the limit = something? Is the question asking you to find f(x) such that [itex]\lim_{x->\inf} \frac{f(x)}{x} = 5[/itex]?
  6. Jun 22, 2009 #5
    Yes indeed I'll fix it.

    No, it just wants me to prove the second limit equals 5.
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