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Calculus I
© 2007 Paul Dawkins
1
http://tutorial.math.lamar.edu/terms.aspx
Preface
Here are the solutions to the practice problems for my Calculus I notes. Some solutions will have
more or less detail than other solutions. The level of detail in each solution will depend up on
several issues.
If the section is a review section, this mostly applies to problems in the first
chapter, there will probably not be as much detail to the solutions given that the problems really
should be review.
As the difficulty level of the problems increases less detail will go into the
basics of the solution under the assumption that if you’ve reached the level of working the harder
problems then you will probably already understand the basics fairly well and won’t need all the
explanation.
This document was written with presentation on the web in mind.
On the web most solutions are
broken down into steps and many of the steps have hints.
Each hint on the web is given as a
popup however in this document they are listed prior to each step.
Also, on the web each step can
be viewed individually by clicking on links while in this document they are all showing.
Also,
there are liable to be some formatting parts in this document intended for help in generating the
web pages that haven’t been removed here. These issues may make the solutions a little difficult
to follow at times, but they should still be readable.
The
Limit
1. For the function
()
3
2
8
4
x
fx
x

=

answer each of the following questions.
(a)
Evaluate the function the following values of
x
compute (accurate to at least 8 decimal
places).
(i)
2.5
(ii)
2.1
(iii)
2.01
(iv)
2.001
(v)
2.0001
(vi)
1.5
(vii)
1.9
(viii)
1.99
(ix)
1.999
(x)
1.9999
(b)
Use the information from
(a)
to estimate the value of
3
2
2
8
lim
4
x
x
x
ﬁ


.
(a)
Evaluate the function the following values of
x
compute (accurate to at least 8 decimal
places).
(i)
2.5
(ii)
2.1
(iii)
2.01
(iv)
2.001
(v)
2.0001
(vi)
1.5
(vii)
1.9
(viii)
1.99
(ix)
1.999
(x)
1.9999
[Solution]
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View Full Document Calculus I
© 2007 Paul Dawkins
2
http://tutorial.math.lamar.edu/terms.aspx
Here is a table of values of the function at the given points accurate to 8 decimal places.
x
PQ
m
x
PQ
m
2.5
3.38888889
1.5
2.64285714
2.1
3.07560976
1.9
2.92564103
2.01
3.00750623
1.99
2.99250627
2.001
3.00075006
1.999
2.99925006
2.0001
3.00007500
1.9999
2.99992500
(b)
Use the information from
(a)
to estimate the value of
3
2
2
8
lim
4
x
x
x
ﬁ


.
[Solution]
From the table of values above it looks like we can estimate that,
3
2
2
8
li
m3
4
x
x
x
ﬁ

=

2. For the function
()
2
23
1
t
Rt
t
+
=
+
answer each of the following questions.
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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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