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)
In
a fix? Try solutions to assignment six.
Assignment 7
6.1 6, 58 (making the graph using technology will
suffice for this question - and c is the distance from the centre of
the outside wheel)
6.2 15, 49 (second changed from 50)
6.3 51, 57
6.4 13, 45
Be
glad that this one doesn't go to eleven … see solutions to assignment seven.