L06 - Lecture 6 One-sided/Infinite Limits, Continuity...

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Unformatted text preview: Lecture 6 One-sided/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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L06 - Lecture 6 One-sided/Infinite Limits, Continuity...

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