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!

Real Analysis: Coninuity2

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove that f(x) = 3*x + 11 is uniformly continuous.

    2. Relevant equations

    x,y in S and |x-y| < a imply |f(x)-f(y)| < e

    3. The attempt at a solution

    following the book I get to

    f(x) - f(y) = 3(x-y)

    i just dont know how to chose e in this case..

    would it be |f(x) - f(y)| < e/3

    any pointers are greatly appreciated
  2. jcsd
  3. Nov 12, 2008 #2


    Staff: Mentor

    The idea is that you can make f(a) arbitrarily close to f(b) by specifying how close a must be to b, regardless of where a and b are.

    So if you wanted f(a) to be within 0.03 of f(b), how close must a be to b?
  4. Nov 12, 2008 #3
    You already did, you just forgot to say that the proof was done. By the time you get to | f(x) - f(y) | = | 3(x-y) | then look, you know you can make (x-y) smaller than some d, how small? Smaller than e/3. Then it follows that for e>0
    if |(x-y)| < d = (e/3) then |3(x-y)| < 3*(e/3) = e
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Real Analysis: Coninuity2
  1. Real analysis (Replies: 3)

  2. Real analysis (Replies: 0)

  3. Real analysis (Replies: 16)

  4. Real Analysis (Replies: 1)

  5. Real Analysis (Replies: 5)