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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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View Full Document Computing Limits
In the previous
section
we saw that there is a large class of function that allows us to use
( ) ( )
lim
xa
f
xf
a
→
=
to compute limits.
However, there are also many limits for which this won’t work easily.
The
purpose of this section is to develop techniques for dealing with some of these limits that will not
allow us to just use this fact.
Let’s first got back and take a look at one of the first limits that we looked at and compute its
exact value and verify our guess for the limit.
Example 1
Evaluate the following limit.
2
2
2
41
2
lim
2
x
xx
x
x
→
+
−
−
Solution
First let’s notice that if we try to plug in
2
x
=
we get,
2
2
2
20
lim
x
→
+−
=
−
So, we can’t just plug in
to evaluate the limit.
So, we’re going to have to do something
else.
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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.
 Spring '11
 Tadius

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