UC11A-3.1

UC11A-3.1 - Math 11A - Calculus w/ Applications I Text:...

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Math 11A - Calculus w/ Applications I Text: Neuhauser, , 2nd edition Calculus for Biology and Medicine Chapter 3 - Limits and Continuity 3.1 Limits Motivation -- finding the slope of a tangent line to a curve. Definition: the limit of f(x) as x approaches c is L , denoted , lim BÄ- 0B œP ab means that can be made arbitrarily 'close' to whenever is 0B P B sufficiently 'close' to - . Alternate notation: as 0B ÄP BÄ- example: example: lim lim BÄ% BÄ$ Š‹ $B  & œ œ [table] [factor] B* B$ # Notation: If a limit exists, we say to ; if the limit does P0 B P converges not exist, we say that as tends to . B - diverges Note: the limit is determined by values of 'near' , and not 'at' c. œ - B œ example: 0B œ œ B * # B$ if if BÁ$ %B œ $ One-sided limits: when approaches from the right. lim BÄ- B - when approaches from the left (or from below). lim BÄ- B - example: find , where lim BÄ% œ B" B% #B( B% # if if example: lim BÄ! lBl B œ
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Math 11A - Calculus w/ Applications I Text: Neuhauser, , 2nd edition Calculus for Biology and Medicine 3.1 Limits (continued)
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This note was uploaded on 07/24/2009 for the course MATH 11A taught by Professor Migliore during the Winter '06 term at UCSC.

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UC11A-3.1 - Math 11A - Calculus w/ Applications I Text:...

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