CalcNotes0207-page9 - (Section 2.7: Precise Definitions of...

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(Section 2.7: Precise Definitions of Limits) 2.7.9 PART D: “LONG-RUN” LIMITS The precise definition of lim x ± a fx () = L can also be modified for “long-run” limits. Again, the only changes are the x -intervals where we look for winners. (See red type.) Our x -intervals of interest will be unbounded. • Therefore, we will use interval form instead of absolute value notation when describing these x -intervals. • Also, instead of using ± , we will use M (think “Million”) and N (think “very Negative”) to denote “points of no return.” The Precise - M Definition of lim x ²³ = L For L ± ± , and for a function f defined on an interval of the form
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