CalcNotes0207-page8

CalcNotes0207-page8 - R and for a function f defined on an...

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(Section 2.7: Precise Definitions of Limits) 2.7.8 PART C: ONE-SIDED LIMITS The precise definition of lim x ± a fx () = L can be modified for left-hand and right-hand limits. The only changes are the x -intervals where we look for winners. (See red type.) Our x -intervals of interest will no longer be symmetric about a . • Therefore, we will use interval form instead of absolute value notation when describing these x -intervals. • Also, we will let ± represent the entire width of an x -interval, not just half the width of a punctured x -interval. The Precise - ² Definition of a Left-Hand Limit at a Point For a , L ±
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Unformatted text preview: R , and for a function f defined on an interval of the form c , a ( ) , where c is a real constant and c < a , lim x ± a ² f x ( ) = L ± ± > , ± > ± x ± a ² ³ , a ( ) ´ f x ( ) ² L < µ ¶ · ¸ ¹ . The Precise-Definition of a Right-Hand Limit at a Point For a , L ± R , and for a function f defined on an interval of the form a , c ( ) , where c is a real constant and c > a , lim x ± a + f x ( ) = L ± ± > , ± > ± x ± a , a + ( ) ³ f x ( ) ´ L < ¶ · ¸ ¹ . Left-Hand Limit Right-Hand Limit (Figure 2.7.g) (Figure 2.7.h)...
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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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