# Urgent Help!

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• November 20th 2008, 12:03 PM
pkr
Urgent Help!
http://i453.photobucket.com/albums/q...188/math11.jpg

Any answers to this would be greatly appreciated, bit of assessed work i'm really struggling on.
• November 20th 2008, 12:25 PM
ThePerfectHacker
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?