Assignments
Suggestions to the Student
The problems in this book are a bit different from the usual calculus
textbook problems. They are not intended to be harder although some
may well be. They are intended, instead, to help you better
understand the concepts of calculus and how to apply them. None of
these problems asks simply for a computation, and some ask for no
computation at all. Instead, they may ask you to do one of the
following: Apply a concept or technique you have just learned in a
mildly novel context; combine concepts or techniques that you have seen only
in isolation before; give a graphical interpretation of the behaviour of a
function; make an inference, from a graph or a table of data, about a
function or a physical relationship.
When you begin working on these problems, you may feel that you do not
know how to get started on a problem or where you should end up.
That's only natural. In fact, some of the problems can be
approached in a variety of ways and have no single answer. Since the
purpose of all the problems in this volume is to help you develop a better
understanding of calculus, a good way to get started is to see if you
understand the question. Talk it over with a classmate and see if the
two of you have the same interpretation. If you don't check in the
textbook to see if you have the right meanings for the crucial words in the
problem. Draw a picture, if possible, to illustrate the problem.
If you encounter a function that is hard to graph, use a computer or a
graphing calculator to draw the graph. In fact, all uses of
computers and calculators are legitimate in working on these problems.
If you are still stuck, talk it over some more with a classmate or ask
for a discussion in class, but be prepared to offer the thoughts you have
developed about the problem.
The keys to getting the most out of these problems are thinking, discussing
and writing. When you recognize a concept or technique that is likely
to be involved in a problem, ask yourself what you know about it and how it
might be applied, and be prepared to reread your textbook or lecture notes
to refresh your understanding Then test your ideas by discussing them
with a classmate or in class. Finally, write up your conclusions in complete
English sentences that convey your understanding as clearly as you know how.
With practice, you will discover that discussing and writing promote
clear thinking and thus help you develop a better understanding of the
material that you are studying.
Assignments
Assignment 1
7.1 40, 62
7.2 70, 88
7.3 122, 136
Please carefully read solutions for all assignments. The
first is a good place to start.
Assignment 2
7.5 80, 84
7.6 112, 116
8.2 54, 70
8.3 66, 68
8.4 44, 57 (57, while odd, does not count as a selected
exercise)
You do what you do; here are solutions to assignment
two.
Assignment 3
8.5 30, 44
8.6 66 (ok a break here, since we didn't do much with this
section)
8.7 24, 28a
8.8 65 (scored as two problems, one for a and one for b)
For you, from me - solutions to assignment three.
Assignment 4
10.8 20, 46
10.1 104, 120
10.2 82, 84
10.3 42, 50
10.4 48, 56
You want more? Here are solutions to assignment
four.
Assignment 5
10.5 60, 64
10.6 44, 66
10.7 26, 58
10.9 38, 56
10.10 26, 38
Results? How to derive? Check out solutions
to assignment five.
Assignment 6
7.4 36, 44
9.1 20, 26
11.1 32, 38
In a fix? Try solutions to assignment six.
Assignment 7
11.2 44, 46
11.3 68
11.4 16, 28
11.5 16, 20
This one goes to eleven … see solutions to assignment
seven.