1. ## Limits

Use the Divergence Criterion for Functional Limits corollary:
(Let $f$ be a function defined on $A$, and let $c$ be a limit point of $A$. If there exist two sequences $(x_n)$ and $(y_n)$ in $A$ with $x_n \not= c$ and $y_n \not= c$ and lim $x_n$=lim $y_n$= $c$ but lim $f(x_n) \not=$lim $f(y_n)$, then we conclude that the functional limit $lim_{x\rightarrow c} f(x)$ does not exist.)the
to show that the following limit does not exist.

$lim_{x\rightarrow 0}$ $|x|/x$

Thanks!

(Let $f$ be a function defined on $A$, and let $c$ be a limit point of $A$. If there exist two sequences $(x_n)$ and $(y_n)$ in $A$ with $x_n \not= c$ and $y_n \not= c$ and lim $x_n$=lim $y_n$= $c$ but lim $f(x_n) \not=$lim $f(y_n)$, then we conclude that the functional limit $lim_{x\rightarrow c} f(x)$ does not exist.)the
$lim_{x\rightarrow 0}$ $|x|/x$
take $f(x) = \frac {|x|}{x}$, $c = 0$, $x_n = \frac 1n$ and $y_n = - \frac 1n$