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.
fx if fc f x for all x near c. 2. x c is a relative (or local) minimum of fx if fc f x for all x near c. 1st Derivative Test If x c is a critical point of fx then x c is 1. a rel. max. of fx if fx 0 to the left of x c and fx 0 to the right of x c. 2.
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