# L05 - Lecture 5 — Limits and slopes A real sequence is a...

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Unformatted text preview: Lecture 5 — Limits and slopes A real sequence is a function a defined from the set of natrual numbers to the reals, normally written as a (1) ,a (2) ,a (3) ,... or a 1 ,a 2 ,a 3 ,... or just as { a n } . Examine the sequences 3 , 3 . 1 , 3 . 14 , 3 . 141 , 3 . 1419 , ... 1 2 , 2 3 , 3 4 , 4 5 , 5 6 , ... 1 , , 1 , 1 , , 1 , 1 , 1 , , 1 , 1 , 1 , 1 , ,... 1 , 1 + 1 2 , 1 + 1 2 + 1 3 , 1 + 1 2 + 1 3 + 1 4 , ... We say a real sequence a n has limit L if, given any small distance , we can show that far enough out in the sequence, the distance between L and each of the sequential values a n is smaller than . What appear to be the limits of the sequences above? Can we say it with certainty? The Pharmacist. A pharmacist researches a drug that is ineffective at levels less than 100 mg and potentially dangerous above 250 mg. The average human body disposes of 20 % of the remaining drug every hour. Based on these facts, the pharmacist recommends that the drug should be taken at a dose of 100 mg every three hours. Examine this decision by looking at the drug level, D n , after the n th dose is taken. Drug level (mg) Hour 0 Hour 1 Hour 2 Hour 3 Hour 6 177.41 Hour 9 190.84 Hour 18 197.71 Hour 27 201.23 Hour 36 203.03 Formula...
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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.

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L05 - Lecture 5 — Limits and slopes A real sequence is a...

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