1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Advanced Calc. Continuity problem

  1. Jun 24, 2010 #1
    So I've been trying to figure this out. The question is:

    If the limit x->infinity of Xn=Xo

    Show that, by definition, limit x->infinity sqrt(Xn)=sqrt(Xo)

    I'm pretty sure I need to use the epsilon definition.
    I worked on it with someone else and we think that what we have to show is the this:

    Want to show:
    For all e>0 there is an N>0 s.t. for all n>N, |sqrt(Xn) - sqrt(Xo)|<e

    I just don't know how to show this.

  2. jcsd
  3. Jun 24, 2010 #2


    Staff: Mentor

    Does this help?
    [tex]\sqrt{x_n} - \sqrt{x_0} = \sqrt{x_n} - \sqrt{x_0} \frac{\sqrt{x_n} + \sqrt{x_0}}{\sqrt{x_n} + \sqrt{x_0}} = \frac{x_n - x_0}{\sqrt{x_n} + \sqrt{x_0}}[/tex]
  4. Jun 24, 2010 #3
    ^ If it does, I can't see it. I feel like I need to find an N in terms of e to show that this si continuous or something.
  5. Jun 24, 2010 #4


    Staff: Mentor

    You're given that
    [tex]\lim_{n \to \infty} x_n = x_0[/tex]

    What does that mean in terms of the epsilon-N definition of a limit?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook