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Epsilon Delta limits

  • Thread starter jrjack
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  • #1
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Homework Statement


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]


Homework Equations





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]
 

Answers and Replies

  • #2
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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:
  • #3
HallsofIvy
Science Advisor
Homework Helper
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Homework Statement


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]


Homework Equations





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]
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

I don't undestand it's use in this problem, if the other part gave me [itex]\delta=2[/itex]
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]?
 
  • #4
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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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