Calculus MaximusNotes 1.1: Limits & ContinuityGoing where we can’t go . . .This interruption to the flow of the graph ofgin Example 2 is called aremovable point discontinuity, oraholein the graph ofg.Simply evaluating a function at a particular value is insufficient for understanding the behavior of sometypes of functions at that point, especially functions with discontinuities at those points.There is, therefore,a need to come up with another method that will circumvent the possibility of going directlytoa location,but ratherapproachingthat location from either side of it.This is the limit, and it has its own notation asyou will seeThe Limit is a Notion of MotionExample 3:Suppose you wanted to safely and smooooothly cross achasm in your car.What three things would you need?Would you be able to do so in the situation depicted in thephoto to the right?What is missing?If you were to build the bridge, would you know exactlywhere to build it to make crossing the chasm in a car acontinuously smooth undertaking?
