Question 1122228
limit as x approaches 7 for |x-7|/(x-7)


the absolute value of x-7 will always be positive.


x-7 itself will be negative when x is less than 7 and positive when x is greater than 7.


sinced the limit from the left is not equal to the limit from the right, the limit doesn't exist.


the limit itself will approach 1 from the right and will approach -1 from the left.


here's a graph of the function.


<img src = "http://theo.x10hosting.com/2018/090101.jpg" alt="$$$" >