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Math Help - Continuity

  1. #1
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    Continuity

    I need help finding examples of two types of functions:
    1. A continuous function on (0,1) that is not bounded, and
    2. A bounded continuous function on (0,1) that is not uniformly continuous

    Any help is vastly appreciated.
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  2. #2
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    Quote Originally Posted by spoon737 View Post
    I need help finding examples of two types of functions:
    1. A continuous function on (0,1) that is not bounded, and
    2. A bounded continuous function on (0,1) that is not uniformly continuous
    1) Let f(x) = 1/x on (0,1)
    2) Let f(x) = sin(1/x) on (0,1)
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