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Limits 2
take $z=\frac 1x$ Then $z \to \infty $ as $x \to 0$
then the given limit becomes :
$\lim_{z \to \infty} \frac{z}{e^z} [\frac {\infty}{\infty}]$
Now, $\lim_{z \to \infty} \frac{1}{e^z} $ [using L'Hospital]
$=0$