# Problem Sets

### Suggestions to the Student

Our problems 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    40
7.2    70
7.3    124
7.5    80, 84
7.6    112
Problem Set 1B
7.1    44
7.2    86
7.3    136
7.5    76, 90
7.6    114 - explain why

What we've waited for … solutions to the first problem set

Problem Set 2A
8.1    66, 70
8.2    64
8.3    44
8.4    30, 48
8.5    66
8.6    28
8.7    22
Problem Set 2B
8.1    64, 72
8.2    66
8.3    38
8.4    32, 44
8.5    66
8.6    34 to the nearest ¢
8.7    16

Sorry about the rain delay, here are solutions to problem set 2

Problem Set 3A
10.1    120
10.2    26, 81,84
10.3    44, 48
10.4    48, 56
10.5    60, 66
Problem Set 3B
10.1    118
10.2    24, 82, 83
10.3    42, 50
10.4    46, 58
10.5    62, 64

A couple hours of delay, but here are solutions for you to enjoy to problem set 3

Problem Set 4A
10.6    42, 66
10.7    28, 50
10.8    20, 42
10.9    38, 56
10.10  28, 40
Problem Set 4B
10.6    44, 62
10.7    26, 54
10.8    22, 46
10.9    36, 54
10.10  26, 38

Trying to be on time for this one, solutions to problem set 4.

Problem Set 5A
7.4    34, 42
9.1    18, 28
11.1    32, 38
11.2    46
11.3    68
11.4    14
11.5    18
Problem Set 5B
7.4    24. 44
9.1    20, 26
11.1    34, 36
11.2    44
11.3    68
11.4    16
11.5    16

For one last time, here are problem set 5 solutions