# How do you show the limit does not exist #lim_(x->6)(|x-6|)/(x-6)#

##### 1 Answer

Mar 31, 2018

See explanation.

#### Explanation:

First if we write the function without the absolute value we get:

#f(x)={(1;x>6),(-1;x<6):}#

So if we calculate the left- and rightside limits we get:

Leftside limit:

Rightside limit:

The leftside limit is not equal to the rightside limit, so the limit does not exist.