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Show that f is continious at 0 (easy but confused)

  1. Jun 24, 2013 #1
    1. The problem statement, all variables and given/known data

    let f be a function t: lf(x)l≤lxl
    show that f is continious at 0

    3. The attempt at a solution
    it's easy to see that f(0)=0
    now [itex]\forall[/itex]E>0 [itex]\exists[/itex]α>0 [itex]\forall[/itex]x[itex]\in[/itex]D: lxl<α => lf(x)-f(0)l<E now in the solution manual they just put it like this : since lxl<α implies lf(x)-(f(0)=0)l<E then f i s continious at a , what i'm not getting is that they didn't give alpha a value they just want from x<alpha to the result ? i've been studying limits since 2012 so this is a weird issue to me , please help
    Last edited by a moderator: Jun 24, 2013
  2. jcsd
  3. Jun 24, 2013 #2


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    Staff: Mentor

    Just take α=E.
  4. Jun 25, 2013 #3
    thanks i forgot a bit about the first definition that's why i had trouble ,i've got it now
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