1. Not finding help here? Sign up for a free 30min 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!

Epsilon-delta proof of one sided infinite limit.

  1. Jun 28, 2013 #1
    1. The problem statement, all variables and given/known data
    proof this limit:
    [itex]\lim_{x\rightarrow 1^+}\frac{1}{(x-1)(x-2)}=-∞[/itex]


    2. Relevant equations



    3. The attempt at a solution

    So for every [itex]N < 0[/itex], I need to find a [itex]\delta > 0[/itex] such that
    [itex]0 < x - 1 < \delta \Rightarrow \frac{1}{(x-1)(x-2)} < N[/itex]

    Assuming [itex]0 < x - 1 < 1[/itex], I get [itex]-1 < x - 2 < 0[/itex], and [itex]-\frac{1}{x-2}>1[/itex].

    Assuming [itex]0 < x - 1 < -\frac{1}{N}[/itex], I get [itex]-(x-1) > \frac{1}{N}[/itex], [itex]-\frac{1}{x-1} < N[/itex], and [itex]\left(-\frac{1}{x-1}\right)\left(-\frac{1}{x-2}\right) < N\left(-\frac{1}{x-2}\right)[/itex], but then I got stuck.
     
  2. jcsd
  3. Jun 28, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hi reinloch! welcome to pf! :smile:
    the trick is to choose δ so that 1/(x - 2) is less than a fixed number :wink:
     
  4. Jun 28, 2013 #3
    Thanks. I am stuck with the right choice for [itex]\delta[/itex]. I choose 1 and [itex]-\frac{1}{N}[/itex], and it didn't seem to work.
     
  5. Jun 28, 2013 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    choose δ so that x doesn't get too close to 2 :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Epsilon-delta proof of one sided infinite limit.
Loading...