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Real analysis questions.

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Please give examples

    -functions continuous nowhere, continuous at one point

    – functions differentiable everywhere but with discontinuous derivative

    – Examples of uniformly continuous functions, functions not uniformly continuous

    – Combinations of the above. For example, find a function, f : [0, 1] ! [0, 1], having the
    intermediate-value property but continuous at only one point

    thank you very much!

    2. Relevant equations
    Rolle’s theorem
    Mean-value theorem
    Cauchy mean-value theorem

    3. The attempt at a solution

    I have trouble to start it . Please help.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 12, 2010 #2


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    Homework Helper

    hi gordon_0451, welcome to PF - you need to show your attempts & people will try & help
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