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!

Limits Question Definition

  1. Mar 19, 2008 #1
    If I have a function lets say lim x->5 f(x) that

    f(5) Does not exist, because if I give a value of x which equals the limit , there is no anymore limit?


    I hope the question is understandble.

    Thanks in advance.
     
  2. jcsd
  3. Mar 19, 2008 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The existence of a limit of a function [itex]f(x)[/itex] at a point [itex]x=c[/itex] has nothing to do with whether the function is actually defined there. That's because a control is built into the definition of a limit that prevents [itex]x[/itex] from taking on the value [itex]c[/itex] as we take the limit. That's what the [itex]0<|x-c|<\delta[/itex] is there for, to ensure that the distance between [itex]x[/itex] and [itex]c[/itex] is strictly positive.
     
  4. Mar 19, 2008 #3
    Yeah, I like to think of it as making sure that it is approaching c from both sides.

    A good example might be [tex]\frac{\sqrt{x+1} -1}{x}[/tex]. The limit exists at c > 0 and the answer is 0 but the you can't just plug that in.

    if you let x = -0.1 f(x) is 5.132 and -0.01 f(x) .5013, and -0.001 f(x) is .5001 (from the left), and x is .001, f(x) is 0.4999, x is 0.1, f(x) is 0.4988 (from the right), and so on.

    When you study continuity I think it really helps clear things up in regards to the existence of limits.
     
  5. Mar 19, 2008 #4
    Thank you very much
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Limits Question Definition
  1. Definition of a Limit (Replies: 1)

Loading...