On-line Math 21

Example 2 Let

f(x) = ì í î 3x+1 if x ³ 1 x+2 if x < 1 .

Then

lim x® 1  f(x)

does not exist.

Solution

The reason it doesn't exist is that, as you approach from the left ( x < 1 ), the values get towards 3, while from the right ( x > 1) , the values get towards 4. This does have what are called one-sided limits (on either side).

Copyright (c) 2000 by David L. Johnson.