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Math Help - understanding continuety proof..

  1. #1
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    understanding continuety proof..

    suppose e>0 b>0

    so if
    |x-a|<b >>> |x-a|<|x|<b
    |f(x)-f(a)|<e >>> |f(x)-f(a)|<|f(x)|<e

    from that step they do write same things all over again and conclude that.

    lim (f(x))=f(a)
    x->infinity


    how to get from the step i showed to this conclution?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by transgalactic View Post
    suppose e>0 b>0

    so if
    |x-a|<b >>> |x-a|<|x|<b
    |f(x)-f(a)|<e >>> |f(x)-f(a)|<|f(x)|<e

    from that step they do write same things all over again and conclude that.

    lim (f(x))=f(a)
    x->infinity


    how to get from the step i showed to this conclution?
    There must be something missing from your hypothesis.

    Why does |x-a|<b\implies|x|<b

    Counter example x=1 and a=50

    What exactly is the context of this?
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  3. #3
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    i ment that if
    |x|<b
    then this is definitely true
    |x-a|<b
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by transgalactic View Post
    i ment that if
    |x|<b
    then this is definitely true
    |x-a|<b
    This is only true if x and a are of opposite signs... x=3,a=-1,b=4 is one example and x=-3,a=1,b=4 is another.
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