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Math Help - Urgent Help!

  1. #1
    pkr
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    Urgent Help!



    Any answers to this would be greatly appreciated, bit of assessed work i'm really struggling on.
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  2. #2
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    Quote Originally Posted by pkr View Post
    The idea for the first parts is that if \epsilon > 0 and x is a fixed point then we can take \delta > 0 small enough such that |x-y|^{\alpha} < \epsilon for all |x-y| < \delta. Therefore, |f(x)-f(y)| \leq |x-y|^{\alpha} < \epsilon. Thus, f is continous.

    In the second part if \alpha > 1 then |f(x)-f(y)| \leq |x-y|^{\alpha} then | [f(x)-f(y)]/[x-y] | \leq |x-y|^{\alpha - 1}. Notice the LHS has form of a derivative. Thus, what can you conclude?
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