Unit U Big Question #2

2. What is a limit? 

A limit is the intended height of a function at a certain value. Basically what this means is it is the y-value at which a function is approaching on the x-axis but may or may not reach it but it is intended to reach it.

 When does a limit exist? When does a limit not exist?

A limit exists as long at the same height (y-value) is reached from both the left and the right. In other words, the limit exists if both the right hand limit and the left hand limit are the same. If the graph does not break at a certain x-value, then the limit exists. For instance, at a hole, the limit exists because the intended height was still reached, even if the "diner" (in the car analogy) is not there.

 

   

 

(Image from curvebank.calstatela.edu)

What is the difference between a limit and a value? 

 

(Image from Unit U SSS packet)  

 The limit is the intended height and the value is the real or actual height. As you can see in the picture above, the limit and value are two different things. We can have the limit equal the value on a continuous graph because the limit is always reached and there are not breaks OR holes in the graph.