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Prove [itex]\lim_{a\to 0}\frac{1}{a} = \infty[/itex]

  1. Oct 15, 2012 #1
    1. The problem statement, all variables and given/known data


    Prove [itex]\lim_{a\to 0^+}\frac{1}{a} = +\infty[/itex] under the [itex]\epsilon[/math] definition of a limit.

    2. The attempt at a solution

    Well, I can't do [itex]\frac{1}{a} - \infty < \epsilon[/itex] can I? Otherwise it's just obvious that it's infinity ..
     
  2. jcsd
  3. Oct 15, 2012 #2

    Zondrina

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    Homework Helper

    For this particular problem you need to alter your definition abit since |f(x) - ∞| < ε translates into a useless statement.

    You want to use this definition :

    [itex]\forall M>0, \exists δ>0 \space | \space 0<|x-c|<δ \Rightarrow f(x) > M[/itex]

    What this definition essentially means is that we can find a delta such that the function grows without bound.

    Start by massaging the expression f(x) > M into a suitable form |x-c| < δ which will give you a δ which MIGHT work.

    Then take that δ and show that it implies f(x) > M.
     
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