1. ## Help with intervals...

I have a problem that says:

Sketch the interval (a,b) on the x axis with the point Xo inside. Then find a value of delta > 0 such that for all x, 0 < abs value(x-Xo) < delta -> a<x<b

I am given a=1 b=7 Xo=2

How would I find the value of delta? Thanks for the help!!

2. Originally Posted by KarlosK
I have a problem that says:

Sketch the interval (a,b) on the x axis with the point Xo inside. Then find a value of delta > 0 such that for all x, 0 < abs value(x-Xo) < delta -> a<x<b

I am given a=1 b=7 Xo=2

How would I find the value of delta? Thanks for the help!!
The distance from x to $\displaystyle x_0$ has to be less than the distance from x to a or the distance from x to b. $\displaystyle \delta$ has to be less than the smaller of $\displaystyle b-x_0$ $\displaystyle a- x_0$.

3. .

I did what you said and came up with

5 and -1

So does that mean I could just choose any number that is less than -1 for the ?

4. Originally Posted by KarlosK
.

I did what you said and came up with

5 and -1

So does that mean I could just choose any number that is less than -1 for the ?
No. We need $\displaystyle \delta >0$.
In these problems $\displaystyle \delta =\min\left\{|x_0-a|,|x_0-b|\right\}$.

5. .

So it comes out to 1, 5

so it has to be a number less than one? Does it matter which number I choose?

6. Originally Posted by KarlosK
.

So it comes out to 1, 5 so it has to be a number less than one?
Does it matter which number I choose?
Absolutely, it makes a real different.
Do you understand what the concept of minimum implies?
What is the minimum here, $\displaystyle \{1,5\}?$
That is your $\displaystyle \delta$.