ModifyingBelow lim With x right arrow $0$limx$0$StartAbsoluteValue x EndAbsoluteValuexequals$=0$

by first evaluating

ModifyingBelow lim With x right arrow $0$ Superscript minuslimx$0$StartAbsoluteValue x EndAbsoluteValuex

and

ModifyingBelow lim With x right arrow $0$ Superscript pluslimx$0+$StartAbsoluteValue x EndAbsoluteValuex.

Recall that

StartAbsoluteValue x EndAbsoluteValue equals left brace Start $2$ By $2$ Matrix $1$st Row $1$st Column negative x $2$nd Column if x less than $02$nd Row $1$st Column x $2$nd Column if x greater than or equals $0$ EndMatrixx$=$

$$x$$if$$x$<0$x$$if$$x$0$

$.$