Calculus Volume 2
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973
12.1 SOLUTIONS
CHAPTER TWELVE
Solutions for Section 12.1
Exercises
1. The distance of a point P = (x, y, z ) from the yz -plane is |x|, from the xz -plane is |y |, and from the xy -plane is |z |.
15.1 SOLUTIONS
1185
CHAPTER FIFTEEN
Solutions for Section 15.1
Exercises
1. The point A is not a critical point and the contour lines look like parallel lines. The point B is a critical point and is a
6.1 SOLUTIONS
421
CHAPTER SIX
Solutions for Section 6.1
Exercises
1. See Figure 6.1.
F (0) = 1
F (0) = 1
1
F (0) = 0
1
x
1
F (0) = 0
x
1
Figure 6.1
Figure 6.2
2. See Figure 6.2.
3. See Figure 6.3.
1
F
8.1 SOLUTIONS
CHAPTER EIGHT
Solutions for Section 8.1
Exercises
1. Each strip is a rectangle of length 3 and width x, so
Area of strip = 3x,
so
5
5
Area of region =
= 15.
3 dx = 3x
0
0
Check: This are
13.1 SOLUTIONS
CHAPTER THIRTEEN
Solutions for Section 13.1
Exercises
1. The vectors are a = i + 3j , b = 3i + 2j , v = 2i 2j , and w = i + 2j .
2. a
b
c
d
e
= 2i + j ,
= 2i ,
= 2i ,
= 2i + 2j ,
= 2i j
14.1 SOLUTIONS
CHAPTER FOURTEEN
Solutions for Section 14.1
Exercises
1. If h is small, then
fx (3, 2)
With h = 0.01, we nd
fx (3, 2)
f (3 + h, 2) f (3, 2)
.
h
f (3.01, 2) f (3, 2)
=
0.01
3.012
(2+1)
10.1 SOLUTIONS
CHAPTER TEN
Solutions for Section 10.1
Exercises
1. Let f (x) =
1
= (1 x)1 . Then f (0) = 1.
1x
f (x) = 1!(1 x)2
f (x) = 2!(1 x)3
f (0) = 1!,
f (0) = 2!,
f (x) = 3!(1 x)4 f (0) = 3!,
f
9.1 SOLUTIONS
717
CHAPTER NINE
Solutions for Section 9.1
Exercises
1. The terms look like powers of 2 so we guess sn = 2n . This makes the rst term 21 = 2 rather than 4. We try instead
sn = 2n+1 . If
Vlatko Babic
7th Hour
Title: To Kill a Mockingbird
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Plot: The book tells a story about segregation in America. Throughout the whole book, Scout
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Mrs. Schexnayder
English II-7th Hour
7 February 2014
In The Scarlet Letter written by Nathaniel Hawthorne, Pearl is a character who serves as
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Vlatko Babic
Professor Laura Segura
English 101
21 September 2016
Peer Review: Cassidy
After reading Identity, the overall essay is very smooth and detailed. The story of identity
fits perfect
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Vlatko Babic
Professor Laura Segura
English 101
13 September 2016
In Nancy Mairs student paper On Being A Cripple, the author thoroughly describes
living with a disability. She mentions powerf
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Author:
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CLID/Section: Your-CLID & section-number go here
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Vlatko Babic
Mrs. Langley
UNIV 100
21 September 2016
After playing more games this week, I have learned a lot more about hidden math in
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Vlatko Babic
Mrs. Langley
UNIV 100
9 September 2016
While playing more games, I have discovered a lot more hidden math in classic games.
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Math 301 Section 001: Calculus II
Class Policy
Instructor: Dr. Chris Ryan
Ofce: Maxim Doucet 313 D, Hours: MTRF 9:30-10:30 AM, 5:00-6:00 PM
Contact info:
E-mail: [email protected]
Phone (ofce):