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Limit homework issue

  1. Jul 12, 2012 #1
    1. The problem statement, all variables and given/known data
    If f(x)=x2 prove that [tex] \lim_{x \to 2} f(x)= 4[/tex]
    Solution given:
    We must show that given any ε >0, find δ >0 such that |x2-4|<ε when 0<|x-2|<δ

    Choose δ≤1 so that <|x-2|<1
    -----------------------------------------------
    Confuse between the word 'find' and 'choose'.
     
  2. jcsd
  3. Jul 12, 2012 #2

    LCKurtz

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    Re: Limits

    ##|x^2-4|=|(x+2)(x-2)|=|x+2|\cdot |x-2|##. So if ##|x-2|<1## how big can ##|x+2|## be? Then once you figure that out, how much smaller than 1 does ##|x-2|## need to be to make the whole thing less that ##\epsilon##?
     
  4. Jul 13, 2012 #3

    HallsofIvy

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    Re: Limits

    You can "find" many values of [itex]\delta[/itex] that will work and then "choose" one of those. That is the same as "finding" a value.
     
  5. Jul 13, 2012 #4
    Re: Limits

    Thanks. My confusion must be interpreting the word "find" as calculate in usual mathematics or physcis problems.
     
    Last edited: Jul 13, 2012
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