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Homework Help: Limit as X approaches ∞ of (X)(sin(1/X))

  1. Oct 4, 2015 #1
    1. The problem statement, all variables and given/known data
    lim (x)(sin(1/x))

    2. Relevant equations

    3. The attempt at a solution
    The correct answer is 1, however I do not understand why. I thought that 1/∞ is essentially 0 and sin(0) = 0 so the whole limit would be 0. When I graphed it, the limit did seem to approach 1 though. I don't understand why it doesn't work out algebraically.
  2. jcsd
  3. Oct 4, 2015 #2
    UPDATE: wait never mind, i just realized how you can do it algebraically
  4. Oct 4, 2015 #3


    Staff: Mentor

    You have x becoming unbounded while sin(1/x) is approaching 0. This is the indeterminate form [0 * ∞], meaning that we can't say without taking the limits what will happen.
  5. Oct 4, 2015 #4
    Ohh, I wasn't aware that 0 * ∞ is considered indeterminate form as well, but that's good to know now though, thank you!
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