Limit
A function 
is said to have a limit 
if, for all 
, there exists a 
such that
whenever 
.
A Lower Limit
is said to exist if, for every
, 
for infinitely many values of 
and if no numberless than 
has this property. An Upper Limit
is said to exist if, for every
, 
for infinitely many values of and if no numberlarger 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 
.See also Central Limit Theorem, Continuous, Discontinuity, L'Hospital's Rule,Lower Limit, Upper Limit
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.
- Cardinality
- Cardinal Number
- Cardioid
- Cardioid Caustic
- Cardioid Evolute
- Cardioid Inverse Curve
- Cardioid Involute
- Cardioid Pedal Curve
- Cards
- Carleman's Inequality
- Carlson-Levin Constant
- Carlson's Theorem
- Carlyle Circle
- Carmichael Condition
- Carmichael Function
- Carmichael Number
- Carmichael's Conjecture
- Carmichael Sequence
- Carmichael's Theorem
- Carmichael's Totient Function Conjecture
- Carnot's Polygon Theorem
- Carnot's Theorem
- Carotid-Kundalini Fractal
- Carotid-Kundalini Function
- Carry