A function is said to have a limit if, for all , there exists a such that whenever .

is said to exist if, for every , for infinitely many values of and if no number less than has this property.

An Upper Limit

is said to exist if, for every , for infinitely many values of and if no number larger than has this property.

Indeterminate limit forms of types and can be computed with L'Hospital's Rule. Types
can be converted to the form by writing

Types , , and are treated by introducing a dependent variable , then calculating lim . The original limit then equals .

**References**

Courant, R. and Robbins, H. ``Limits. Infinite Geometrical Series.'' §2.2.3 in
*What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.*
Oxford, England: Oxford University Press, pp. 63-66, 1996.

© 1996-9

1999-05-25