Transcription of Calculus Cheat Sheet - Lamar University
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Calculus Cheat Sheet - Lamar University
Calculus Cheat Sheet Visit for a complete set of Calculus notes. 2005 Paul Dawkins Limits Definitions Precise Definition : We say ()limxafxL = if for every 0e> there is a 0d>such that whenever 0xad<-< then ()fxLe-<. Working Definition : We say ()limxafxL = if we can make ()fx as close to L as we want by taking x sufficiently close to a (on either side of a) without letting xa=. Right hand limit : ()limxafxL+ =. This has the same definition as the limit except it requires xa>. Left hand limit : ()limxafxL- =. This has the same definition as the limit except it requires xa<. Limit at Infinity : We say()limxfxL = if we can make ()fx as close to L as we want by taking x large enough and positive. There is a similar definition for ()limxfxL - = except we require x large and negative. Infinite Limit : We say ()limxafx = if we can make ()fx arbitrarily large (and positive) by taking x sufficiently close to a (on either side of a) without letting xa=.
Basic Properties and Formulas If fx and g x are differentiable functions (the derivative exists), c and n are any real numbers, 1. cf cf x
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