Problem Sets
Suggestions to the Student
The problems we choose from the 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
1.2 4, 14, 28, 33
1.3 62, 65
1.6 6, 14
2.1 38
2.2 20, 43
Problem Set 1B
1.2 6, 12, 26, 34
1.3 63, 64
1.6 8, 12
2.1 40
2.2 22, 44
Look, it's solutions to problem set 1 (this version). The problems on next version will appear after it is due.
Problem Set 2A
1.4 56, 64
2.3 52, 58
2.4 21, 24
2.5 30, 48
2.6 23, 44
3.1 12
Problem Set 2B
1.4 50, 62
2.3 54, 56
2.4 22, 23
2.5 32, 46
2.6 24, 43
3.1 8
Here are the solutions to problem set 2, notice that all the problems that you did for either problem set are now in one of these documents.
Problem Set 3A
2.7 22
3.2 42, 50
3.3 48
3.4 46, 54
3.7 32. 36
Problem Set 3B
2.7 20
3.2 44, 48
3.3 50
3.4 48, 52
3.7 30, 38
What you see, solutions to problem set 3. Also check out the daily problems - lots of material there.
Problem Set 4A
1.5 42, 56
2.8 26, 42
3.5 32, 38
3.6 34, 42
Problem Set 4B
1.5 40, 58
2.8 28, 40
3.5 34, 37
3.6 32, 48
What's more, it's solutions to problem set 4. Someone really should read the daily problems. That's my opinion.
Problem Set 5A
4.1 50
4.2 28
4.3 18, 20, 24
4.4 50, 58
4.5 41, 56
Problem Set 5B
4.1 48
4.2 30
4.3 16, 22, 26
4.4 54, 56
4.5 42, 55
Problem Set 6A
4.6 44, 55
4.7 48
5.1 36, 44
5.2 8, 20
5.3 26, 34
Problem Set 6B
4.6 42, 56
4.7 42
5.1 38, 41
5.2 10, 18
5.3 24, 36