Consider the left sided limit.

Make a table to show the behavior of the function as approaches from the left.

As the values approach , the function values approach . Thus, the limit of as approaches from the left is .

Consider the right sided limit.

Make a table to show the behavior of the function as approaches from the right.

As the values approach , the function values approach . Thus, the limit of as approaches from the right is .

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

Evaluate limit as x approaches 0 of arctan(1/x)