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Math Help - intervals

  1. #1
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    intervals

    assuming that g is continuous on [a,b] and that g(t) is greater than or equal 0 for all t in [a,b]

    suppose that there is some y in [a,b] such g(y)>0. since g is cont on [a,b], a subinterval [c,d] containing y can be found for which g(t) > 1/2 (g(y)) where c<t<d.


    may i know how g(t) > 1/2 (g(y)) is obtained?

    thanks
    Last edited by alexandrabel90; January 10th 2011 at 05:16 PM. Reason: typo
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    assuming that g is continuous on [a,b] and that g(t) is greater than or equal 0 for all t in [a,b]

    suppose that there is some y in [a,b] such g(y)>0. since g is cont on [a,b], a subinterval [c,d] containing y can be found for which g(t) > 1/2 (g(y)) where c<t<d.


    may i know how g(t) > 1/2 (g(y)) is obtained?

    thanks

    Use limits: continuity \Longrightarrow g(x)\xrightarrow [x\to y]{}g(y)\Longrightarrow \exists \delta > 0 \,\,s.t.\,\, |x-y|<\delta \Longrightarrow |f(y)-f(x)|<\frac{1}{2}f(y)

    (here, \epsilon=\frac{1}{2}f(y) ), thus...

    Tonio
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