How do you find the limit of #x / |x|# as x approaches #0#?

1 Answer
Alan P.
Jun 1, 2016

The limit depends upon which side of #0# that #x# approaches from

Explanation:

If #x# is negative but approaching 0
#color(white)("XXX")#written #lim_(xrarr0^-)#
then
since #x/abs(x)=-1# for all negative values of #x#
#color(white)("XXX")lim_(xrarr0^-) x/abs(x)=-1#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If #x# is positive but approaching 0
#color(white)("XXX")#written #lim_(xrarr0^+)#
then
since #x/abs(x)=+1# for all positive values of #x#
#color(white)("XXX")lim_(xrarr0^+) x/abs(x)=1#

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