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!

Prove using the precise definition of the limit

  1. Mar 17, 2014 #1
    1. The problem statement, all variables and given/known data

    lim x→2 (x2+1) = 5

    2. Relevant equations

    0 < |x-a| < delta

    |f(x) - L| < ε

    3. The attempt at a solution

    0 < |x-2| < delta

    |x2-4| < ε

    |(x-2) (x+2)| < ε

    |x-2| |x+2| < ε..................and I am stuck here, any help
     
  2. jcsd
  3. Mar 17, 2014 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Continuing your analysis:$$
    |x-2|<\frac \epsilon {|x+2|}$$You are trying to get the right side small by getting ##x## close to ##2##. So you don't want the denominator to get close to ##0##. Can you keep it away from ##0## if ##x## is close to ##2##? That's the idea you need to pursue.
     
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: Prove using the precise definition of the limit
Loading...