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Homework 8 (MATH 1199 Fall 2019)
1. Let

$C$ be the top half of the circle

$|z|=3$ . Use the ML-inequality to bound

$\left| \displaystyle\int_C \dfrac{z+1}{z^2-5} \mathrm{d}z \right|$ .
2. Let

$C$ be the circle

$|z+1|=2$ . Use the ML-inequality to bound

$\left| \displaystyle\int_C \dfrac{3z-1}{(z+1)^2+1} \mathrm{d}z \right|$ .