CalcNotes0207-page5

CalcNotes0207-page5 - (Section 2.7: Precise Definitions of...

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(Section 2.7: Precise Definitions of Limits) 2.7.5 PART B: THE PRECISE ± - ² DEFINITION OF A LIMIT AT A POINT The Precise - Definition of a Limit at a Point (Version 1) For real constants a and L , and for a function f defined on an open interval containing a , possibly excluding a itself, lim x ± a fx () = L ± for every > 0 , there exists a > 0 such that, if 0 < x ± a < (that is, if x is “close” to a ), then ± L < (that is, is “close” to L ). Variation Using Interval Form We can replace 0 < x ± a < with: x is in a ± , a + , x ± a . We can replace ± L < with: is in L ± , L + . Related Notation a ± ± a is a member of the set of real numbers a , L ±
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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