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Homework Help: Use delta-epsilon proof

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data
    limit as x goes to 0 of x^2 sin(1/x)=0

    2. Relevant equations
    Use delta-epsilon proof

    3. The attempt at a solution
    So |f(x)-L|=|x^2 sin(1/x)|=|x^2||sin(1/x)| and I know that sin(1/x) is bounded by one. I am not sure how to finish because of the x^2.
  2. jcsd
  3. Mar 23, 2008 #2


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    … one step at a time … !

    Hi Michelle! :smile:

    I can't make out whether you've got the answer or not.

    You must practise stating things clearly.

    And thinking clearly! One step at a time!

    First step: what do you think the limit is?

    Second step: why do you think it's that (in layman's terms)?

    Third step: put second step into delta-epsilon form.

    :smile: … three steps to happiness! … :smile:
    Have a go!
  4. Mar 23, 2008 #3
    the limit is 0, I think this because it given, also I know sin(1/x) is bounded by so that leaves x^2, so if I choose my epsilon to be sqrt epsilon. then when you square the x then x^2<epsilon
  5. Mar 23, 2008 #4


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    … oh happiness … !

    Very good! :smile:

    hmm … now we've got you thinking clearly, how about writing clearly?

    You see … you meant "… my delta to be sqrt epsilon", didn't you?

    … and it would be much better if you got into the habit of actually writing "Given any epsilon > 0, then for any x with |x| < √epsilon, |x^2sin(1/x) |≤ x^2 < epsilon; therefore lim(x¬0) = 0", instead of just thinking it! :rolleyes:
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