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Could someone help me through this problem?

Consider $I_{\epsilon}=\displaystyle\oint_{C_{\epsilon}} z^{\alpha}f(z)\,dz,\qquad \alpha>-1,\qquad \alpha$ real where $C_{\epsilon}$ is a circle of radius $\epsilon$ centered at the origin and $f (z)$ is analytic inside the circle.

Show that $\displaystyle\lim_{\epsilon \to 0}{I_{\epsilon}}=0$

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That's the worst question title I've seen in a long time. You're supposed to write something that describes the question, not just arbitrarily take the first $n$ characters of the text! – Henning Makholm Apr 25 '12 at 14:26
up vote 0 down vote accepted

What's going on with your when you shrink your circle? What is true of your function when you go from one circle to a smaller one? The function is analytic inside the circle, so it dosen't have a singularity inside, so. You are shrinking your contour to a.... Point

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