Answer
$0$
Work Step by Step
$\lim _{z\rightarrow \infty }\left( e^{-2z}+\dfrac {2}{z}\right) =e^{-\infty }+\dfrac {2}{\infty }=\dfrac {1}{e^{\infty }}+\dfrac {2}{\infty }=0+0=0$
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