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If f(c) = infinity and c is in [a,b]

  1. May 8, 2005 #1
    if f(c) = infinity and c is in [a,b]
    is it equivalent to saying
    f is not cont. at c ??? because infinity is undefined???


    Thanks
    k.cv
     
  2. jcsd
  3. May 8, 2005 #2

    Pyrrhus

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    It's NOT continuous.
     
  4. May 8, 2005 #3
    SO it would also imply that if a function is cont. in a finite interval [a,b] then its bounded?
     
  5. May 8, 2005 #4

    Pyrrhus

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    Yes, it has superior bound. There exist a number N such that f(x)<= N for every x in [a,b]. Geometricly speaking this means there exist a paralel line to the horizontal axis. And of course a inferior bound, the same for a number N such that f(x) >= N for every x in [a,b].
     
    Last edited: May 8, 2005
  6. May 8, 2005 #5

    HallsofIvy

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    If a function f is continuous on a closed and bounded interval, then it is bounded. You implied "closed" when you said [a,b] but I want to make sure that is clear.
     
    Last edited: May 8, 2005
  7. May 8, 2005 #6

    matt grime

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    If you're claiming f is a function from [a,b] to R, then f is not defined at c, and actually f therefore isn't a function, never mind a continuous one.
     
  8. May 13, 2005 #7
    nice...I just invented the mean value theorom!!
     
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