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Epsilon-Delta proof help

  1. Aug 26, 2009 #1
    I need to show that:

    [itex]\lim_{x \to 0} x^{2}sin(1/x)=0[/itex]

    Using the epsilon-delta method. I figured delta=sqrt[epsilon] would make the limit hold, but wanted to be sure. Thanks in advance.
  2. jcsd
  3. Aug 26, 2009 #2
    I believe it can be show that if [tex]\epsilon[/tex] = [tex]\delta[/tex]

    [itex]abs(x^{2}sin(1/x))\leq x^{2}[/itex] < [tex]\epsilon[/tex]
  4. Aug 26, 2009 #3
    [tex]\delta = \sqrt{\varepsilon} [/tex] is ok too, |sin(...)| will be always less or equal to 1, so [tex]\varepsilon \left|\sin(1/\sqrt{\varepsilon})\right| \leq \varepsilon[/tex]
  5. Aug 26, 2009 #4
    This is more sufficient.:)
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