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单词 Limit
释义

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.


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