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Unformatted text preview: Lecture 6 — Onesided/Infinite Limits, Continuity Suppose an optical scanner uses reflected light to track its distance D from an object. For the objects shown, write the formula for D ( x ) and sketch its graph, where x is the horizontal distance traveled. D ( x ) = What is the limit of D ( x ) as x approaches 2 ? Right/Left Limits Definition . We say a function f ( x ) has limit L as x approaches number a from the right (left) if, given any small distance , we can show that the distance between every f ( x ) and L is smaller than , once the distance between a and x > a ( x < a ) is chosen small enough. We write lim x → a + f ( x ) = L or f ( x ) → L as x → a + ( x → a ) ( x → a ) Right and left limits provide additional information when a limit does not exist, so we provide them whenever possible. Note: lim x → a f ( x ) = L if and only if For the scanner function, lim x → 2 D ( x ) = lim x → 2 + D ( x ) = Doomsday: Friday 13, 2026 In an (in)famous result, population data was used to argue that global population was not growing in proportion to population size N (which would be exponential growth), but closer to a faster power function N 1+ r . A differential equation leads to a population function of the form P ( t ) = K r √ T t where r,K,T are constants....
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This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Continuity, Limits

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