How do I evaluate the following one sided limits? Do they even exist?

Question

lim (x -> 2) x / |x|


lim (x -> 0) x / |x|

Thank you for any help!

Answer 1

lim (x -> 2) x / |x| = 1
coz 2+ and 2- are >0

lim (x -> 0) x / |x|
at 0+ ans= 1 at 0- ans=-1
so limit in this case does not exist

* * * * * * Explanation * * * * * *
lim (x -> 2) x / |x| = x/x = 1
at 2+ ans = x/x = 1
at 2- ans = x/x = 1
limit exists

lim (x -> 0) x / |x|
at 0+ ans= x/x =1
at 0- ans=x/-x = -1
limit does not exist

Answer 2

lim (x -> 2) x / |x| = 1
It does not matter whether x approaches 2 from below or above, since |x| = x as long as x is possitive.
lim (x -> 0) x / |x|
= 1 when x approaches 0 from above (same as the first problem),
= -1 when x approaches 0 from below (since |x| = -x as long as x is negative).