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Continuity at a point problem

  1. Apr 7, 2012 #1
    I'm working on a problem as part of exam revision, but i've run into a bit of trouble so far. The problem is;
    Give an (ε,δ) proof that f(x) = 1/[itex]\sqrt{10 - x^2}[/itex] is continuous at x = -1




    The attempt at a solution
    So far what i've gotten is f(x) - f(-1) = 1/([itex]\sqrt{10 - x^2}[/itex]) - 1/3
    = (3 - ([itex]\sqrt{10 - x^2}[/itex]))/(3[itex]\sqrt{10 - x^2}[/itex])
    = ((x^2) - 1)/(3[itex]\sqrt{10 - x^2}[/itex])

    Then from here i've gotten -2 < x < 0 → 10 - x^2 > 6
    i'm lost from where to go from here though i just can't see a way though, any help will be greatly appreciated.
     
    Last edited: Apr 7, 2012
  2. jcsd
  3. Apr 8, 2012 #2

    tiny-tim

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    welcome to pf!

    hi ferret93! welcome to pf! :smile:
    the standard trick is to write that as (x+1) times the rest …

    you use ε,δ to minimise (x+1), and some other limit to kepp the rest bounded :wink:
     
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