Shawn Magee
Assignment 2
1. The picture I chose is from the gallery on National Geographic which is called Changing Seas
taken by Massimo Vitali. This image illustrates Anthropocene because humans hav
Math 222: Final Review Packet
Disclaimer 1. This review packet should only be viewed as supplementary to (and not a replacement for)
studying the notes, old homeworks, quizzes, exams, etc. For example
Math 222: Midterm 2 Review Packet
Complex Numbers
1. Show that sin(3) = 3 cos2 () sin() sin3 (),
and derive a similar formula for cos(3).
2. Find all real and complex solutions to the following polyno
4. (a)
f (x) = x3 + x 1, f (x) = 3x2 + 1, C1 = 0
Use Newtons method:
Cn+1 = Cn
f (Cn )
f (Cn )
.
Then,
C2 = C1
f (C1 )
f (0)
1
=0
=0
=1
f (C1 )
f (0)
1
C3 = C2
f (1)
1
3
f (C2 )
=1
=1 =
f (C2 )
f (
Answer Keys for Even Numbers
$ 11.4
4. converges by the Direct Comparison Test;
1 +cos n
n2
n 2 and the p-series n 2 converges.
2
1
12. converges by the Limit Comparison Test (part 2) when compared w
Math 222 Sec. 363, 367 (Circle one)
Quiz #2
Name :
1. (1) Calculate the Taylor series T f(x) where f(x) =
(Hint: Use geometry series).
1+2x
(2) For which real numbers x does the Taylor series converge
Math 222 Sec. 363, 367 (Circle one)
Name :
Quiz #3
1. Find and draw all real and complex solutions of z 4 + 2z 2 = 3.
2. Use cos = (ei + ei )/2 and/or sin = (ei ei )/2i to evaluate an indefinite integ
Shawn Magee
Section: 306
Assignment #1
1.
William Cronon explained wilderness as a land that is not receiving any work done by
mankind at that point in time. He believes that Apostle Islands today are
Shawn Magee
Assignment 3
2.
After reading Redford and Sandersons Extracting Humans from Nature and Schwartzman et
al.s Arguing Tropical Forest Conservation: People versus Parks, they both want whats b
Shawn Magee
Discussion 306
Assignment 4 Population
1.
I believe that the world is becoming over populated. According to the article Billions and
Billions that on Halloween in 2011 the world population
Shawn Magee
Discussion Section 306
Assignment 5
1) Malthus theory about what causes environmental crisis is overpopulation in an
area. He believed that the over population was the reason for the lack
Shawn Magee
Discussion = 306
Assignment 7 Adaptation
3) The change in temperature and precipitation is from global warming which is mainly caused
by humans and environmental issues. One of the reason
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Discussion - 306
Assignment 9 Agriculture
1.
Global agricultural production is increasing with the worlds population. With more
people living the more of a demand agriculture becomes. The
Shawn Magee
Assignment 10
1) Small scale organic agriculture is harvesting of crops and livestock on a small piece of
property and done by not using expensive technology equipment. This form of farmin
Math 222 Sec. 363, 367 (Circle one)
Name :
Quiz #5
1. A can is lying on the plane P with equation x1 + 3x2 + x3 = 6. Gravity pulls the can down,
and exerts a force given by
0
= 0 .
f
mg
(a) Find a no
Math 222 Sec. 363, 367 (Circle one)
Quiz #4
1. Find the function y of x which satisfies the conditions:
Name :
dy
dx
+ (1 + 3x 2 )y = 0, y(1) = 1.
2. Find the general solution y(t) of the differential
Answer Keys for Even Numbers
$ 10.1
6. foci are (0, 5), vertices are (0, 3)
8. foci are (0, 5), vertices are (0, 2), asymptotes are y=2x
10. p=(3/2), focus is (0, 3/2), directrix is y=-(3/2)
18.
x2
16
4. (a) Note that this equation is a linear rst order dierential equation.
dy
2y = x
dx
I (x) = exp( 2dx) = e2x
(1)
(2)
dy 2x
e
2ye2x = xe2x
dx
(3)
Dx (e2x y ) = xe2x
(4)
Take integrals both sides:
e