Limits at Infinity - Notes

Limits at Infinity - Notes - Preface Here are my online...

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Preface Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus. I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from an Algebra or Trig class or contained in other sections of the notes. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. 1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn calculus I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. You will need to find one of your fellow class mates to see if there is something in these notes that wasn’t covered in class. 2. Because I want these notes to provide some more examples for you to read through, I don’t always work the same problems in class as those given in the notes. Likewise, even if I do work some of the problems in here I may work fewer problems in class than are presented here. 3. Sometimes questions in class will lead down paths that are not covered here. I try to anticipate as many of the questions as possible when writing these up, but the reality is that I can’t anticipate all the questions. Sometimes a very good question gets asked in class that leads to insights that I’ve not included here. You should always talk to someone who was in class on the day you missed and compare these notes to their notes and see what the differences are. 4. This is somewhat related to the previous three items, but is important enough to merit its own item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!! Using these notes as a substitute for class is liable to get you in trouble. As already noted not everything in these notes is covered in class and often material or insights not in these notes is covered in class.
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Limits At Infinity, Part I In the previous section we saw limits that were infinity and it’s now time to take a look at limits at infinity. By limits at infinity we mean one of the following two limits. ( ) ( ) li m lim xx f x fx ¥ fi-¥ In other words, we are going to be looking at what happens to a function if we let x get very large in either the positive or negative sense. Also, as we’ll soon see, these limits may also have infinity as a value. First, let’s note that the set of Facts from Infinite Limit section also hold if the replace the lim xc with lim x fi¥ or lim x fi-¥ . The proof of this is nearly identical to the proof of the original set of facts with only minor modifications to handle the change in the limit and so is left to the reader.
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This note was uploaded on 02/05/2011 for the course CALCULUS/C 202 taught by Professor Tadius during the Spring '11 term at Benedictine KS.

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Limits at Infinity - Notes - Preface Here are my online...

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