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!

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


    User Avatar
    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 :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Epsilon-Delta Proof
  1. Epsilon-Delta Proof (Replies: 3)

  2. Delta epsilon proof (Replies: 5)