Calculus_Cheat_Sheet_Limits_Reduced

Calculus_Cheat_Sheet_Limits_Reduced - Calculus Cheat Sheet...

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Calculus Cheat Sheet Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. © 2005 Paul Dawkins Limits Definitions Precise Definition : We say () lim xa f xL = if for every 0 ε > there is a 0 δ > such that whenever 0 <−< then fx L −< . “Working” Definition : We say lim f = if we can make f x as close to L as we want by taking x sufficiently close to a (on either side of a ) without letting x a = . Right hand limit : lim f + = . This has the same definition as the limit except it requires x a > . Left hand limit : lim f = . This has the same definition as the limit except it requires x a < . Limit at Infinity : We say ( ) lim x f →∞ = if we can make ( ) f x as close to L as we want by taking x large enough and positive. There is a similar definition for ( ) lim x f →−∞ = except we require x large and negative. Infinite Limit : We say ( ) lim fx =∞ if we can make ( ) f x arbitrarily large (and positive) by taking x sufficiently close to a (on either side of a ) without letting x a = . There is a similar definition for ( ) lim = −∞ except we make ( ) f x arbitrarily large and negative.
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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