Why do we find the limit of a function?

Answer 1

Typically, it's to give you an idea of a function graphically. Sometimes you deal with functions that are really hectic in design and they don't really have all the points smoothly in place (for example, a graph with an empty point or ^, a peak). A limit gives you an idea of what's happening with the graph as you get close to that point or area (as with infinity not being an actual point), hence the "as x approaches N," N being either some number, or negative or positive infinity.