Learning Resources

Investigation 7: Instantaneous Velocity & Focus F: Limit Notation

• The limit does not exist if the same finite value is not obtained from both sides.
• A point can be approached even if it does not exist on the graph. The x-value is only approached from both sides; it is not reached.
• The limit is the finite y-value that is approached.

It is essential that you see the difference in the way the term limit is used in this Focus as opposed to Investigation 7. While the concept is the same, it is used in a different manner. In Investigation 7, you worked with the limit of the slope as the points got closer together. In Focus F, however, you found the limiting value of y as x approached a given value.