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 |.
So A is closest to the yz -plane, since it has the smal
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 local
maximum; the point C is a saddle point.
2. (a) P
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 (0) = 1
F (0) = 1
1
x
F (0) = 0
1
x
F (0) = 0
1
Figure
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 area can also be computed using Length Width = 5 3 = 15.
2
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
3. The vector we want is the displacement from Q to P
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)
32
(2+1)
0.01
= 2.00333.
With h = 0.0001, we get
fx (3
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 (4) (x) = 4!(1 x)5 f (4) (0) = 4!,
f (5) (x) = 5!(1 x)6
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 we now check, we get the terms 4, 8, 16, 32, 64, . . .,
Vlatko Babic
7th Hour
Title: To Kill a Mockingbird
Author: Harper Lee
Publication Date: 1960
Plot: The book tells a story about segregation in America. Throughout the whole book, Scout
Finch deals with many problems with the people around her. The book is
Vlatko Babic
Babic 1
Mrs. Schexnayder
English II-7th Hour
7 February 2014
In The Scarlet Letter written by Nathaniel Hawthorne, Pearl is a character who serves as
a symbol. Throughout the story she is viewed as many things. Some believe she is a demon chi
Babic 1
Vlatko Babic
Mrs. Langley
UNIV 100
9 September 2016
While playing more games, I have discovered a lot more hidden math in classic games.
Checkers is another simple game with hidden math. As you play the game, you must keep track
of the pieces that
7'4
Math 301 Test 4 Page 2 of 5 11/16/2015
2 5 8 11 14 17 . .
1. (10 points) Find the general term of the sequence starting With n : 1.
- Eda-1
a_ in
NH ._._ 3
in am: W TV: ;2_ '
\A-a-HP WW
2. (10 points) Show that the sequence cfw_12722 ~ 25n:i is even
Math 301 Test 3 Page 2 of 6 10/28/2015
1 _
1. (10 points) Use the reduction formula / sinnwdac = ; sinn"1 :Bcosa: + n n 1 / sin" 2 radar:
to evaluate / 5sin4mdm.
3 2
jSSll/q'lol'u '2 5 2:" $391 mm +37; 59m 14%
A I . l
'%<(cfw_u3aw1+ L; K" irMcan -+ E: l
Babic 1
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 perfectly with the goal of the essay. The essay provides a ton
Rhetorical Analysis Graphic Organizer
ENGL 102 Ritorto/ Spring 2017
Name: _ Author: _ Title: _
Argument and Introduction
Hierarchy of Ideas
Audience and Appeals
Lending Credence
Concrete Supporting Evidence
Conclusion
What is the main argument? How is it
Babic 1
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 powerful words such as cripple and handicapped
which effectiv
#
#
#
#
Author:
Your-Name
CLID/Section: Your-CLID & section-number go here
Part I of this lab will use the math library, which means
it must be imported
import math
# Print sin/cos/tan for the "common" angles of 30, 45 & 90 degrees
# Remember, sometimes o
Babic 1
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
games. The game of skip-bo is a good example of a game that centers around number
sequences. The game involves
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: cxr2665@louisiana.edu
Phone (ofce): (337)482-5301
Graphing calculator: A graphing calculato