Explain why f(x) is not continuous at a = 1.

Question

Explain why f(x) =  1/(x−1)   if x doesn't equal 1

                             2            if x does equal one

                    

 

ANSWER: The limit as x approaches a of f(x) does not exist.

 

I get that there's a removable discontinuity, however, I still think the limit exists. 

 

#29, practice test

Answer 1

For a limit to exist the limit from the left must be the same as the limit form the right.

for f(x) = 1/(x - 1), as x approaches 1 from the left the f(x) approaches (has the limit) of -1.

As x approaches 1 from the right f(x) approaches (has the limit) of 1.

 

The limit does not exist.