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 have made this
beach to look beautiful. The sand on Tuscan
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, note that there is no spring-mass
problem in these no
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 polynomials:
a) z 3 6z 2 + 11z 6 = 0
b) z 4 9z 2 + 20 = 0
c)
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 with n 2 , a convergent p-series 0.
n=1
1
1
16. diverges
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 to f(x)?
1
2. Find the fourth degree Taylor polynomial
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 integral
cos 2 .
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 wilderness spots in the
world. The islands may show th
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 best for the
forest and to protect these wild animals. I
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 was seven billion people. Today the
world population i
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 of resources
whether it was food supply or a lack of wa
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 humans cause global warming is by
pollution which gets
Shawn Magee
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 increasing of agricultural has an
impacts on the enviro
Shawn Magee
Assignment 8
1.
2.
3.
4.
5.
6.
Total greenhouse gas emissions = 30
Home energy = 13
Driving & Flying = 11
Food & Diet = 5
Recycling & Waste = 1
Cost to offset your carbon footprints = $405
1. Today, coal is able to provide energy in family hom
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 farming
has been increasing because of the demand for local f
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 normal for the plane P.
n
(b) Decompose the force into a
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 equations:
d2 y
dt2
y = 2et .
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:
e2x y =
xe2x dx
Now, we solve this equation for y.
1
Use