This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
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, Slope, Limits

Click to edit the document details