Problem Sets
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.
Problem Sets
Problem Set 1A
7.1 44
7.2 54, 62
7.3 32
6.1 56
6.2 22, 50, 46
Problem Set 1B
7.1 42 and 46 as one question
7.2 56, 66
7.3 34
6.1 58
6.2 20, 52, 44
These are the solutions to both halves of the first problem set. Please read them thoroughly.
Problem Set 2A
6.3 68, 74
6.4 36
6.5 44
7.3 36
7.4 35, 38
7.5 28, 30
7.6 58
7.7 54
Problem Set 2B
6.3 66, 76
6.4 34
6.5 42
7.3 38
7.4 36, 37
7.5 26, 30
7.6 54
7.7 56
Here are solutions to problem set two. Please read them before the first exam.
Problem Set 3A
9.1 36, 48
9.2 Writing Exercise 2, 42
9.3 42, 58
9.4 40
Problem Set 3B
9.1 38, 46
9.2 Writing Exercise 1, 44
9.3 44, 56
9.4 43
Look what you see, solutions to problem set three.
Problem Set 4A
9.5 Writing Exercise 4, 40
9.6 Writing Exercise 2, 36
9.7 50
9.8 24, 48
9.9 12, 20
Problem Set 4B
9.5 Writing Exercise 2, 42
9.6 Writing Exercise 3, 34
9.7 48
9.8 26, 46
9.9 14, 18
Here are solutions to problem set 4 (and a little more - includes the questions that were unassigned. Feel free to ignore them if you wish.)
Problem Set 5A
8.1 2
8.2 60, 64
8.3 18, 23
10.1 22, (26, 27, 30 as one question)
10.2 26, 42
10.3 10
10.4 56
10.5 28
Problem Set 5B
8.1 4
8.2 58, 66
8.3 20, 24
10.1 24, (25, 28, 29 as one question)
10.2 28, 40
10.3 12
10.4 54
10.5 30
Here are your final problem set solutions (including the omitted problems).