The Mathematics of Financial Modelingand Investment Management

4-PrincipCalculus Page 103 Friday, March 12, 2004 12:39 PM

Principles of Calculus 103

EXHIBIT 4.2 Graphical Presentation of Infinite Limits, Limits from the Left or

Right, and Finite Limits

Note that the notion of limit can be defined only in a continuum. In

fact, the limit of a sequence of rational numbers is not necessarily a

rational number.

CONTINUITY

Continuity is a property of functions, a continuous function being a

function that does not make jumps. Intuitively, a continuous function

might be considered one that can be represented through an uninter-

rupted line in a Cartesian diagram. Its formal definition relies on limits.

A function fis said to be continuous at the point cif

lim fx()= fc()

x→c