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Math Help - Help with intervals...

  1. #1
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    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!!
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  2. #2
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    Quote Originally Posted by KarlosK View Post
    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 x_0 has to be less than the distance from x to a or the distance from x to b. \delta has to be less than the smaller of b-x_0 a- x_0.
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  3. #3
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    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 ?
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  4. #4
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    Quote Originally Posted by KarlosK View Post
    .

    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 \delta >0.
    In these problems \delta =\min\left\{|x_0-a|,|x_0-b|\right\}.
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  5. #5
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    So it comes out to 1, 5

    so it has to be a number less than one? Does it matter which number I choose?
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  6. #6
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    Quote Originally Posted by KarlosK View Post
    .

    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, \{1,5\}?
    That is your \delta.
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