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Limits of functions at infinity

  1. Oct 4, 2009 #1
    Suppose that a function f:R to (0,infinity) has the property that f(x) tends 0 as x tends to infinity. Prove that 1/f(x) tends to infinity as x tends to infinity.

    I don't really know where to start with this problem, I'm assuming it will involve some sort of epsilon proof but that's all I know. Please any help would be great!
     
  2. jcsd
  3. Oct 4, 2009 #2

    statdad

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    Write out what it means when you say that f(x) tends to zero as x tends to infinity, and think about what that means for 1/f(x).
     
  4. Oct 4, 2009 #3
    If f(x) tends to zero as x tends to infinity it means that as x gets progressively larger f(x) gets smaller and smaller thus meaning that 1/f(x) gets larger and lerger but this a proof.
     
  5. Oct 4, 2009 #4

    statdad

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    No, write out the meaning of f(x) going to zero in "epsilon" form. You have the right outline in your second post, but it isn't a proof ("hand waving" would be the description). Start with "[tex] \lim_{x \to \infty} f(x) = 0 [/tex] means that for any [tex] \epsilon > 0 [/tex] ..." and continue.
     
  6. Oct 4, 2009 #5
    the function you have given is defined in certain interval suppose take the generalised soln into consideration and prove for soln
     
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