1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook