Question

How do you a find a limit?

Answer 1

http://www.youtube.com/watch?v=QnJ0jAA6ZWM

Answer 2

Here is an example, but there are several rules for combining terms (e.g. sums and products) and for handling cases where you have division by zero. The limit as h->0 is just one example. To test for other values, you would substitute 0 with that value of interest:

Limits are first used to show that there is a value to which a function will converge and is used to determine whether functions are continuous or differentiable, to name just a couple applications of the limit. To really understand what's going on, you need to understand the logical meaning of the limit, where we try to find deltas for arbitrary epsilons such that a certain condition is met: For every real ε > 0, there exists a real δ > 0 such that for all real x, 0 < | x − p | < δ implies | f(x) − L | < ε.