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- Jan 17, 2013

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__Prove the following__If \(\displaystyle f\) has a simple pole at \(\displaystyle z=c\) and \(\displaystyle C_r\) is any circular arc bounded by \(\displaystyle \theta_1 , \theta_2\) and centered at \(\displaystyle c \) with radius \(\displaystyle r\)

\(\displaystyle \lim_{r \to 0^+} \int_{C_r} f(z) \, dz = i ( \theta_2 - \theta_1 ) \text{Res} (f;c)\)