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Homework Help: Why is my proof wrong? (analysis)

  1. Dec 5, 2012 #1
    I was trying to prove this, but something went wrong and I'm not sure what...

    We know that the greatest value of sin(1/x) can be 1 and the lowest value can be -1...

    We know that the upper darboux sum is...

    [tex]U(f,P) = sup(f[t_{k-1} , t_t]) (t_k - t_{k-1}) = (1) (1-(-1)) = 2[/tex]


    We also know that the lower darboux sum is...

    [tex]L(f,P) = inf(f[t_{k-1} , t_t]) (t_k - t_{k-1}) = (-1) (1-(-1)) = -12[/tex]

    So we know that...

    [tex]U(f,P) - L(f,P) = 2 - (-2) = 4 > \epsilon[/tex]

    Can anybody tell me where I went wrong?

    Thanks in advance
     
  2. jcsd
  3. Dec 5, 2012 #2
    What are you trying to prove in the first place??

    And don't there need to be summations in the [itex]U(f,P)[/itex] and [itex]L(f,P)[/itex]?? How did you choose P anyway?

    I also don't see where -12 comes from. Did you mean -2?

    What is [itex]\epsilon[/itex] supposed to be?
     
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