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Prove using the formal definition of a limit

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove using the formal definition of a limit that Lim x→4 x2 = 16

    2. Relevant equations
    |f(x)-L| and |x-c|
    Using epsilon/delta definition.

    3. The attempt at a solution
    I've got that |x2-16| = |x-4||x+4|
    I'm also pretty sure only |x-4| matters, since it is the same as |x-c|.
    What would delta be? Since there's no coefficient of x to factor out, would delta = epsilon?

    Another note: I really have no idea what I'm doing. I've based all my work off of prior examples, I don't understand how to "prove" the limit using the above information.
  2. jcsd
  3. Feb 11, 2012 #2


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    Hi LOLItsAJ! :smile:

    If eg I specify .001, you have to find a range in which x2 lies between 15.999 and 16.001 :wink:
  4. Feb 11, 2012 #3


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    You might start by using the formal definition of limit for the case you're working on:
    Lim x→4 x2 = 16​
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