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Homework Help: Limits when there is a sine function?

  1. Oct 11, 2013 #1
    1. The problem statement, all variables and given/known data

    lim x-> ∞ xsin(1/x)

    2. Relevant equations

    3. The attempt at a solution

    I know that this is an ∞.0 type limit but I can't figure out how to change the sin function.

    Thank you
  2. jcsd
  3. Oct 11, 2013 #2


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    Science Advisor
    Gold Member
    2017 Award

    [tex]x \sin(1/x)=\frac{\sin(1/x)}{1/x}.[/tex]
  4. Oct 11, 2013 #3
    Ahh thank you! Then you use L'Hopitals Rule?
  5. Oct 11, 2013 #4


    Staff: Mentor

    I wouldn't. This limit is related to this well-known limit
    $$\lim_{t \to 0}\frac{sin(t)}{t}$$
  6. Oct 11, 2013 #5
    What do you mean?
  7. Oct 11, 2013 #6
    Hint 2: Use a substitution, then figure out what the appropriate change in the limit would be.
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