You can see that the x values are less than 2 but getting closer and closer to 2. The second array creates a list of x values and y values which show what happens as we approach from the right. You can see that the x values are greater than 2 but getting closer and closer to 2. The y values are approaching the value 3 from both the left and the right. From this evidence, we can guess that the limit is 3.
Lets look at another case.
Copy and paste the two array commands above, and re-execute them to create left and right approaches to the limit for this function. In this case the left and right limits are different. From the left, the value is 16, while from the right, the value is 13. When the left and right limits disagree, we say that the limit does not exist, since there is no single limit. We've approached limits from a geometric and a numeric point of view.