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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]
    [tex]\delta=2[/tex]
    but how does this part of the equation help me find delta?
    [tex]|f(x)-5|<0.1[/tex]
    [tex]4.9<f(x)<5.1[/tex]

    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

    HallsofIvy

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    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.
     
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