Estimating+limits+from+graphs+or+tables+using+data

Using a graph: Here is a very typical graph where one might be asked to find the limit at a variation of x-values. To evaluate at x=1, one must look to see where the graph of the line approaches from both the left and right side of the point. Both sides do approach the same value, and that value is at 1. This same evaluation process can be used for x=3 and x=4. However, at x=2, the limit from the left approaches a different value than the limit from the right. Therefore, the limit is said to not exist.

Using a Table:

Using a table is much like using a graph. One must look at what the values approach from both the left and right side of the value. This technique may not always be very exact when dealing with fractions and decimals. Again, if the different sides approach different values, then the limit does not exist.