Find the limit, if it exists. lim[x→0+0 ( 8/x − 8/|x|)

Answer 1

OK...then

for x>0 (8/x)-(8/|x|) = 0

and therefore the required right-sided limit is 0.

Please note that the left-sided limit does not exist and the function, therefore, has a non-removable discontinuity at x=0.