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Math Help - Epsilon-Delta continuity proof

  1. #1
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    Epsilon-Delta continuity proof

    http://img34.imageshack.us/img34/198...s123523456.jpg
    I'm trying to work through some examples, but im not sure where the following comes from:

    1. circled in black -- how do i get the δ<1?

    2. circled in red -- how do I get 0<x<2, i.e. x∈(0,2)?

    3. cirlced in blue -- how do i get |x^2+x+3|<9

    Thanks, most appreciated.
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  2. #2
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    Quote Originally Posted by rlkmg View Post
    1. circled in black -- how do i get the δ<1?

    2. circled in red -- how do I get 0<x<2, i.e. x∈(0,2)?

    3. cirlced in blue -- how do i get |x^2+x+3|<9
    1. In these proof, we are free to pick \delta.

    2. If |x-y|<\delta then y-\delta<x<y+\delta so |x-1|<\delta<1 means that 0<x<2.

    3. If x\in (0,2) then |x^2+x+3|<4+2+3
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  3. #3
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    Thanks. The only thing im wondering is..how do I know how to choose δ? what if i choose δ>1 etc.? How do i know what to choose?


    Thanks
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  4. #4
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    Quote Originally Posted by rlkmg View Post
    Thanks. The only thing im wondering is..how do I know how to choose δ? what if i choose δ>1 etc.? How do i know what to choose?
    Why do that?
    You want the proof to work. Choice depends on what works.
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  5. #5
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    sorry, i dont really understand what that part means.

    Lets say i choose:
    δ<2, and |x-1|<2
    then -1<x<3

    instead of 0<x<2 as done in the question.

    So how would i know how to choose δ<1 instead of say δ<2? etc..
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