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Equations that satisfy requested properties

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the equations that satisfy the following properties:

    1) f:(0,infinity) -> R is continuous and bounded, but f has no maximum and no minimum (that is global min and max).

    2) k:[0,infinity) -> R is continuous, but k has no maximum and no minimum (again global min and max).

    2. Relevant equations

    3. The attempt at a solution

    I'm thinking that i need to use a trig function for number 1, but beyond that i'm stumped.
  2. jcsd
  3. Feb 3, 2010 #2


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    Oh, come on. You can try harder than that. 1) is terribly easy. Find a continuous, bounded and monotone function on (0,infinity). A trig function will help for 2), but if you get a good example for 1) you can combine it with a trig function to get 2).
  4. Feb 3, 2010 #3


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