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Homework Help: Epsilon-Delta Proof

  1. May 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Let a rep. any real number greater than 0
    Prove that the limit as x->a of sqrt(x) = sqrt(a)

    I hav to prove the above equation using using an Epsilon-Delta proof but im not sure how to start it off.

    2. The attempt at a solution

    I assumed that if 0<|x-a|<d
    then |f(x) - f(a)|
    = |sqrt(x) - sqrt(a)|

    I am allowed to use basic manipulations of numbers that preserved the equation and also make helper assumption values for delta if needed as long as i account for them in my proof.

    I've been stuck on this question for 3-1/2 hours now so I would really appreciate any help!
  2. jcsd
  3. May 26, 2008 #2


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    Gold Member

    Try multiplying |sqrt(x) - sqrt(a)| by |sqrt(x) + sqrt(a)| /|sqrt(x) + sqrt(a)|
  4. May 26, 2008 #3
    Given epsilon>0, let delta = epsilon*sqrt(a), and remember that sqrt(x) + sqrt(a) >= sqrt(a) if x>=0.
  5. May 27, 2008 #4
    Ah thx a bunch guys, I couldnt figure out the first step for so long!

    cheers :)
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