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