Geometric Interpretation of a Limit

Calculus
Section 1.5

All three cases, according to the late James Stewart, represent the limit of f(x) as x tends to a equals L.

Sorry but I cannot make the connection between the images here and the intuitive definition of a limit.

Can you please explain all three images?
If I am going to get a decent understanding of calculus as a whole, I need to FIRMLY AND POSITIVELY grasp the limit idea.







You say?

 

so, yes all three cases represent the limit of f(x) as x tends to a equals L

 

Thank you. More calculus and college algebra today. By the way, my birthday is on April 5, 2022. I will be 57 years old. So, I called out for tomorrow night. More math tomorrow as well. I return to work Tuesday evening.