# How do you find the limit #lim_(x->0^-)|x|/x# ?

##### 1 Answer

When dealing with one-sided limits that involve the absolute value of something, the key is to remember that the absolute value function is really a piece-wise function in disguise. It can be broken down into this:

# x# , when# x>= 0#

-#x# , when# x< 0#

You can see that no matter what value of

Because our limit is approaching

#lim_(x->0^-)(-x)/x#

Now that the absolute value is gone, we can divide the

#lim_(x->0^-)-1#

One of the properties of limits is that the limit of a constant is always that constant. If you imagine a constant on a graph, it would be a horizontal line stretching infinitely in both directions, since it stays at the same

#lim_(x->0^-)-1 = -1# , Giving us our final answer.