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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentInfinite
Limits
In this section we will take a look at limits whose value is infinity or minus infinity.
These kinds
of limit will show up fairly regularly in later sections and in other courses and so you’ll need to
be able to deal with them when you run across them.
The first thing we should probably do here is to define just what we mean when we sat that a limit
has a value of infinity or minus infinity.
Definition
We say
( )
lim
xa
fx
ﬁ
=¥
if we can make
f(x)
arbitrarily large for all
x
sufficiently close to
x=a
, from both sides, without
actually letting
=
.
We say
( )
lim
ﬁ
= ¥
if we can make
f(x)
arbitrarily large and negative for all
x
sufficiently close to
x=a
, from both
sides, without actually letting
=
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Tadius
 Limits, Limit, Limit of a function, lim g

Click to edit the document details