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 13A
13.1 40
13.2 30
13.3 28, 52
13.4 40
13.5 56
13.6 (22, 28 scored as one question)
13.7 46, 54

Problem Set 13B
13.1 41
13.2 40
13.3 26, 56
13.4 38
13.5 58
13.6 (24, 26 scored as one question)
13.7 44, 52

Here are solutions to Problem Set 13.

Problem Set 14A
14.1 (20, 24 scored as one question), 39
14.2 32
14.3 32, 41
14.4 18
Extra credit for either A or B (not both):  14.1 42
   
Problem Set 14B
14.1 (22, 23 scored as one question), 40
14.2 31
14.3 33, 42
14.4 17  
Extra credit for either A or B (not both):  14.1 42 

Check out these Problem Set 14 solutions. 

Problem Set 15A
15.1 (54, 56 scored as one question)
15.2 39
15.3 2, 85 and graph as in 84
15.4 7, use this plane to approximate nearby points
15.5 46
15.6 36, 48
15.7 50, 35
15.8 24
  
Problem Set 15B
15.1 (57. 58 scored as one question)
15.2 40
15.3 1, 84
15.4 8, use this plane to approximate nearby points
15.5 48
15.6 38, 47
15.7 48, 36
15.8 38

Coming on XM2, we have solutions to Chapter 15 problems.

Problem Set 16A
16.1 8
16.2 30
16.3 29, 42
16.4 34
16.5 12
16.6 24
16.7 18, 30
16.8 32
16.9 14
  
Problem Set 16B
16.1 10
16.2 28 and draw as in 30
16.3 30, 40
16.4 33
16.5 14
16.6 22
16.7 20, 28
16.8 30
16.9 12

  
Here are some solutions to Chapter 16 problems. 

Problem Set 17A
17.1 (12, 16, 32 scored as one question)  
17.2 18, 25
17.3 8, 16, 28

Problem Set 17B
17.1 (14, 18, 30 scored as one question)
17.2 17, 26
17.3 6, 18, 26

And in the end, Chapter 17 solutions appear.