# Consider $I_{\epsilon}=\oint_{C_{\epsilon}} z^{\alpha}f(z)dz$

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
What have you tried? What are your thoughts? Please be thorough. –  Antonio Vargas Apr 25 '12 at 14:37