Important Remarks
1. The material for each test is as follows.
Test #1 - Chapter 6, 7.1, 7.2
Test #2 - 7.3-7.8
Test #3 - Chapter 8
Test #4 - Chapter 9
2. Some of the problems that are assigned require the use
of a graphing utility or a symbolic integ ration utility .
You may omit any part of a problem that requires the use of either of these
utilities. However, all other parts
of each problem should be completed in full. For example, you may omit part (c)
of problem #11 on p.447.
However, you are required to complete parts (a) and (b).
3. Do not give a decimal approximation for an answer when
an exact answer can be given, unless the directions
state otherwise. For example, it would not be acceptable to give 0.707 as the
answer to
.
The answer
that should be given is
4. Some of the homework assignments are very time
consuming. If you do not have time to do every problem
that is assigned, I have two suggestions.
• If you are working out a problem and you get to a point
where you are 100% sure that you can finish the
problem from there, then you may want to skip the rest of that problem.
• If you are 100% sure that you know how to do a problem, you may want to skip
that problem.
5. There is an enormous amount of material that the state
requires in this course. I have no control over this. As
a result, there will be very little class time to go over homework. Questions on
homework will be answered
at the end of each class, if time permits. If you need help on the homework and
I do not have time to go over
it in class, here are a few suggestions.
• Come to my office hours.
• Go to the math lab .
• Purchase the student’s solutions manual .
• Visit the textbook’s website to see what student resources are available.
• Form a study group with some of your classmates.
• Ask a friend for help.
6. The list of problems that are assigned in each section
begins on the next page.
6.1: odd 1-11, odd 15-29, odd 41-45, 57(as sume a ,b,c >
0),59,69,79,81, p.476 #4,#6
Answers to p.476: 4. 1/3 6. 9/2
6.2: odd 1-31, 45,47,51,59,60d,61abc
Hint for #60d: The height of an isosceles right triangle with the hypotenuse as
its base is 1/2 the length of the hypotenuse.
Hint for #61b: The area of a semi circle is
Hint for #61c: The area of an equilateral triangle with sides of length s is
Answer to #60d: 32/3
6.3: odd 1-21, 22,27
Remark: For problems 21 & 22, you may use the washer method.
Answers: 22a.
22b. 20πln5 22c.
6.4: odd 1-19, 20,23ab, 27, odd 31-37, 45,47,53abc
Answers:
7.1 odd 1-53, odd 59-69, 89
7.2: odd 11-41, odd 47-57, 77,83,89,97abc
Hint for #17: First use integration by parts. Then rewrite
using long division or synthetic division .
7.3: odd 3-15, odd 21-41, odd 47-67, 81a,83,85a
7.4: odd 5-15 (For problem #7, another correct answer is
,
odd 19-47, 50,57,61,63,77,79
#9: Assume x > 2. #11: Assume x ≥ 2. #25: Assume x > 3.
Answer to #50:
7.5: odd 1-31, odd 41-45, 49,53
7.6: odd 1-37, 45,49,55,71
7.7: odd 5-47, 51,53, odd 61-67, odd 73-77, 89,91
Hint for #17: Consider 3 cases: n = 1, n = 2, n ≥ 3
#73: There is an error in the answer given in the back of the textbook. The
function has a relative maximum
at
not a relative minimum.
7.8: odd 1-41 (For problem #7, evaluate the integral
without using a graphing utility), 61,69,87, p.551 #82
Hint for #41: Let u =
.
#61: Assume s > 0.
Answer to p.551 #82: 1
8.1: odd 1-19, odd 27-59, odd 63-87, 88, odd 89-93,
113,115
Answer to #88: Monotonic, not bounded
8.2: odd 1-25, odd 33-61, 67,77,85 odd 97-101
8.3: odd 1-7, odd 11-23, 29, odd 53-63
Hint for #29: Examine 3 cases (p = 1, 0 < p < 1, p > 1).
8.4: odd 3-35, 55
8.5: 1, odd 9-55, odd 69-77
Hint for #19: Write out the first few terms of the series and notice that the
series is
Hint for #25: Let
Show
that f is decreasing if n ≥ 2. Thus,
for n ≥ 2.
8.6: odd 1-9, odd 13-67
Hint for #27: Use natural logarithms and L 'Hopital's Rule to evaluate
Hint for #39: Use natural logarithms and L'Hopital's Rule to evaluate
8.7: 5,7 odd 13-29, 35,41,43
8.8: odd 1-37, 47
8.9: odd 1-25, odd 35-39, 43,45
8.10: odd 1-9, odd 13-33, odd 45-53, 57,67
Hint for #3:
= 1, -1, -1, 1, 1, -1, -1, 1, …
9.1: all 1-8, odd 9-75,
81,83,86,91a,92,103,105,113,123,127
Hint for #86: Let d be the distance between the focus and an arbitrary point on
the parabola . Minimizing
d is equivalent to minimizing d2.
Answer to #86: (0,0)
9.2: odd 1-35, odd 39-53, 67,69,73
Remark: For problems 21-31, delete the phrase “use a graphing utility to” from
the directions. This means
that you should sketch the curves without the use of a graphing utility.
9.3: odd 1-15, 17c,19c, odd 25-33, 35,36,37,40,41,77
#35, #36, #37, #40: You may assume that the curves are smooth on the given
intervals.
Hint for #35:
is evaluated on p.492.
Hint for #41: The graph is shown in problem #70 on p.683.
Answers: 36. 
40.
9.4: odd 1-5, 11,13, odd 19-39, 45,47,53,54,59,61, odd 67-71, 72, odd 73-85, all
95-99, 113,115
Remark: For problems 37, 39, and 45, delete the phrase “use a graphing utility
to” from the directions.
This means that you should graph the polar equations without the use of a
graphing utility.
Answer to #54: 
At (2,0),
At 
is
undefined. At 
Answer to #72: See graph below.
9.5: odd 1-21, odd 27-35, 41,43,44,45,47
Remarks: For problems 9, 11, 27, 29, and 31, delete the phrase “use a graphing
utility to” from the directions.
This means that you should graph the polar equations without the use of a
graphing utility.
For problems 45 and 47, change the directions to “Find the length of the graph
over the indicated
interval.” The answers to these problems are given below.
#33, #35, #41: Assume a > 0.
#45: Instead of using trigonometric substitution , you may use theorem 7.2 on
p.510.
#47: Instead of using trigonometric substitution, you may use formula #30 on
p.A26.
Answers: 44. 64 
10.1: odd 1-57, odd 63-73, 79a,81,89,94, odd 99-103
#79a, #81: Ex press your answers in decimal form, rounded to the nearest tenth.
#89: Express your answers in decimal form, rounded to the nearest hundredth.
10.3: 1,2,4, all 9-13, 19,21,22,41,42,45,46,51
Answers: 2a. 22 2b. 116 2c. 116 2d. 
2e. 44 4a. 1 4b. 1 4c. 1 4d. i 4e. 2
22. parallel
