The limit of f(x), as x approaches a, is L lim _x->a f(x) = L if by taking x sufficiently close to a (but not equal to a) we can make the values of f(x) arbitrarily close to L . Notice we do not say what happens if x=a!

Alternately, we say that "f(x)->L as x->a".

There are several generic cases which arise:

• smooth curve
• curve with a corner
• curve with a cusp (vertical asymptote)
• curve with a discontinuity
• curve with infinite oscillation

For a vector valued function, we take a limit, by taking the limit of each component.

Last modified Mon Sep 9 21:22:37 CDT 1996