Question

$f\left(x\right)=\frac{|x|}{x}x\ne 0$
$0x=0$

Check whether $f\left(x\right)$ is continous or not at $x=0$

Answer 1

Let h be a very small positive real number.

${lim}_{h\to 0}\frac{|0+h|}{h}=\frac{h}{h}=1{lim}_{h\to 0}\frac{|0-h|}{h}=\frac{h}{h}=1whenx=0,\frac{\left|x\right|}{x}=0Hencenotcontinuous.$