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Show that $\lim\limits_{x\to 0}e^\frac{1}{x}$ does not exist.

I tried to show this using the epsilon delta definition but couldn't come across a contradiction.

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    $\begingroup$ Hint: Consider the left and right limits. $\endgroup$ – SquirtleSquad May 2 '17 at 4:43
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    $\begingroup$ As $x\to 0^+$, we have $\frac{1}{x}\to +\infty$ and in this case $e^{\frac{1}{x}}\to +\infty$ Whereas if $x\to 0^-$, we have $\frac{1}{x}\to -\infty$ and in this case $e^{\frac{1}{x}}\to 0$ $\endgroup$ – Juniven May 2 '17 at 4:44
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Try this common estimate: $$ e^{\frac{1}{x}}>1+\frac{1}{x} $$ and approach from the left.

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