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 limits

  1. Sep 19, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose [itex]|f(x)-5|<0.1[/itex] when 0<x<5.
    Find all values [itex]\delta>0[/itex] such that [itex]|f(x)-5|<0.1[/itex] whenever [itex]0<|x-2|<\delta[/itex]

    2. Relevant equations

    3. The attempt at a solution
    I know that [tex]0<|x-2|<\delta[/tex]
    [tex] 2-\delta<x<2+\delta[/tex]
    but how does this part of the equation help me find delta?

    I don't undestand it's use in this problem, if the other part gave me [itex]\delta=2[/itex]
  2. jcsd
  3. Sep 20, 2011 #2
    Try translating the problem into plain English, then it will be something like:
    How far can I move from x=2 so that my function won't be too far from 5, while 0.1 is already too far...=)

    BTW, how is this related to limits? [here you need to find appropriate [itex]\delta[/itex]]
    Last edited: Sep 20, 2011
  4. Sep 20, 2011 #3


    User Avatar
    Science Advisor

    You don't need this at all. You are given that [itex]|f(x)- 5|< 0.1[/itex] if 0< x< 5 and you want "|f(x)- 5|< 0.1 if [itex]2-\delta< x< 2+ \delta[/itex]" so the "f" part is the same in both hypothesis and conclusion. Focus on the other part

    Ignore f completely. What value of [itex]\delta[/itex] will guarentee that if [itex]2-\delta< x< 2+ \delta[/itex] then [itex]0< x< 5[/itex]?
  5. Sep 20, 2011 #4
    Thanks, I have been watching the Kahn Academey and you tube videos and I'm starting to grasp this. I take this course on-line through a community college and the instructors lesson was a power point slide with no sound...it was lacking alot of description and any explanation.

    The videos, on the other hand, were very helpful, so is advice on here, Thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook