It's pretty much the first thing you learn to do in calculus.
Here is a simple one:
Limit as x approaches 2
x2 + 3x - 10
------------
x - 2
(x-2)(x+5)
---------------
x - 2x + 5 = 2 + 5 = 7
As x approaches 2, the function approaches 7
That leads into problems like these:
What is the IROC (Instantaneous rate of change) at x = 3
y = x
2 + x