# Epsilon Delta limits

## Homework Statement

Suppose $|f(x)-5|<0.1$ when 0<x<5.
Find all values $\delta>0$ such that $|f(x)-5|<0.1$ whenever $0<|x-2|<\delta$

## The Attempt at a Solution

I know that $$0<|x-2|<\delta$$
$$2-\delta<x<2+\delta$$
$$\delta=2$$
but how does this part of the equation help me find delta?
$$|f(x)-5|<0.1$$
$$4.9<f(x)<5.1$$

I don't undestand it's use in this problem, if the other part gave me $\delta=2$

## Answers and Replies

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 $\delta$]

Last edited:
HallsofIvy
Homework Helper

## Homework Statement

Suppose $|f(x)-5|<0.1$ when 0<x<5.
Find all values $\delta>0$ such that $|f(x)-5|<0.1$ whenever $0<|x-2|<\delta$

## The Attempt at a Solution

I know that $$0<|x-2|<\delta$$
$$2-\delta<x<2+\delta$$
$$\delta=2$$
but how does this part of the equation help me find delta?
$$|f(x)-5|<0.1$$
$$4.9<f(x)<5.1$$
You don't need this at all. You are given that $|f(x)- 5|< 0.1$ if 0< x< 5 and you want "|f(x)- 5|< 0.1 if $2-\delta< x< 2+ \delta$" 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 $\delta=2$

Ignore f completely. What value of $\delta$ will guarentee that if $2-\delta< x< 2+ \delta$ then $0< x< 5$?

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.