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
0.6     38, 65
old     1: For what values of a and b is the limit as x goes to 0 of (tan2x / x^3 + a/x^2 + (sin bx)/x) = 0?
          2: find the limit as x goes to infinity of (1 + 1/x^2)^x.  Support your work with at least two different graphs.
1.1     38, 56 (for #56 - the integral is something we won't know how to do until Chapter 2.  So, for this question - set up the integral.  Then use technology to approximate the value of the integral, then check _that_ answer by showing your work using geometry.  Sorry for the inconvenience - this problem does not belong in this section). 
1.2     15, 54

Please carefully read solutions for all assignments. Now that you are done, here are solutions to assignment one. 

Assignment 2
1.3    43, 49
1.4    44, 48
2.1    45, 49
2.2    28, 32
2.3    41, 43

You do what you do; here are solutions to assignment two.

Assignment 3
2.4    20, 27
2.5    35 explain
2.6    18 (use _Simpson's_ Rule), 45 show the details of the arithmetic sum in both cases. 
2.7    40, 46

For you, from me - solutions to assignment three.


Assignment 4
5.3    15, 25
4.1    36, 42
4.2    16, 48
4.3    7, 45 (changed from 43, which seems impossible)
4.4    24, 29

You want more?  Here are solutions to assignment four.


Assignment 5
4.5    23, 41
4.6    28, 30
5.1    18, 42 (I'm changing the numerator of this question to (x-2)^2, it makes it much easier.  Expect the original to be extra-credit in solutions)
5.2    30 (the 6n in the exponent is a typo, the 6 just doesn't belong there), 46
5.4    29, 57-59 as one

We do what we can together to survive.  Here are solutions to assignment five.


Assignment 6
3.1    None assigned, but pick two from 8-17
3,2    25 & 27 as one, 32 (show full details for the first two steps by hand, feel free to use software for the remaining ones)
3.3    8, 48
3.4    [All counts as two questions] Project #11 - checking with 2020 data and including inflection point.  What is the prediction of your model for 2050? (do NOT pick your own questions for 3.4)


Assignment 7
6.1    6, 58
6.2    15, 50
6.3    51, 57
6.4    13, 45