Answer
$\infty$
Work Step by Step
$\lim _{x\rightarrow \infty }\dfrac {e^{x/2}}{x}=\dfrac {\dfrac {d}{dx}\left( e^{x/2}\right) }{\dfrac {d}{dx}\left( x\right) }=\dfrac {\dfrac {1}{2}e^{x/2}}{1}=\dfrac {1}{2}e^{x /2}=\infty $
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