I dont understand why the limit does not exist at f(3) and limF(x)

Question

I dont understand why the limit does not exist at f(3) and limF(x)...

 

Please click on line below to see the full problem. I just dont understand why the problem (c) is undefined/does not exist. I could not understand the books meaning properly. Please can someone elaborate.

 

http://i60.tinypic.com/1z5ix6r.jpg

 

Thank you.

Answer 1

The "holes" in the graph of the function mean that the function is undefined (has no values) in those points. In example b) the value of the function in 2 is 5 (the solid dot), but the limit (which is the hight of the "hole" pertaining to the graph) is 3. In example c), the function is undefined (has no value, aka the empty circle on the graph), but its limit is 4. In other words, even though the function has no value in that point (the empty circle), the limit is told by the graph (which tells us that as x approaches 3 from both sides, y approaches 4, but it never reaches 4).