Use the graph to find the limit, if the does not exist , explain why.

Question

lim       |x -2|/(x - 2)

x-->2

Answer 1

Step 1:

The expression is .

Observe the graph.

 exists for all values of  except at .

As  tends to  from the left hand side,  tends to .

As  tends to  from the right hand side,  tends to .

Since the left hand limit and right hand limit are not equal, limit does not exist.

Solution:

 does not exist.