Calculus_Cheat_Sheet_Limits

Calculus_Cheat_Sheet_Limits - Calculus Cheat Sheet Limits...

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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 x a f x L fi = if for every 0 e > there is a 0 d > such that whenever 0 x a d < - < then ( ) f x L e - < . “Working” Definition : We say ( ) lim x a f x L fi = 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 x a f x L + fi = . This has the same definition as the limit except it requires x a > . Left hand limit : ( ) lim x a f x L - fi = . This has the same definition as the limit except it requires x a < . Limit at Infinity : We say ( ) lim x f x L fi¥ = 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 x L fi-¥ = except we require x large and negative. Infinite Limit : We say ( ) lim x a f x fi = ¥ 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 = .
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