Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Proof of a limit rule

Tags:
  1. Dec 19, 2017 #1
    Hello, I would like to begin by saying that this does not fall into any homework or course work for me. It is just my interest.
    I need to prove that limit of a constant gives the constant it self. Can some one provide a link? I have exams or I would have searched myself but unfortunately I don't have time. So, I had to post this thread.
     
  2. jcsd
  3. Dec 19, 2017 #2

    jedishrfu

    Staff: Mentor

  4. Dec 19, 2017 #3

    Mark44

    Staff: Mentor

    This is one of the easiest of limits to prove, using the definition of a limit to prove it. If f(x) = k, a constant, can you show that ##|f(x) - f(a)| < \epsilon## when ##|x - a| < \delta##?
     
  5. Dec 22, 2017 #4
    If I take f(a) =k for some interval around x , then |f(x) - f(a)| =0 <E since by definition E >0.
    But will this work?
     
  6. Dec 22, 2017 #5

    Mark44

    Staff: Mentor

    It will work, but you need to say more.
    Someone gives you a value of ##\epsilon > 0##. Can you specify a number ##\delta > 0## so that when ##|x - a| < \delta##, then ##|f(x) - f(a)| < \epsilon##?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...
Similar Threads for Proof limit rule Date
I Proof of series`s tail limit Mar 16, 2017
I Help With Epsilon Delta Proof of multivariable limit Jun 19, 2016
Uniqueness of limit proof Jan 10, 2016
A limit topic proof Dec 31, 2014
Limit Proof Confusion Sep 16, 2014