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Homework Help: 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

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    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.
     
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