(a)
Non-stationarity can be an important determinant of the properties of a series. Also, if two series are
non-stationary, we may experience the problem of spurious regression. This occurs when we
regress one non-stationary variable on a completely unrel
Two.II Linear Independence
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Definition and examples
Linear independence
1.4 Definition A multiset subset of a vector space is linearly
independent if none of its elements is a linear combinat
Solving Linear Systems
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Gausss Method
Linear systems
1.1 Definition
A linear combination of x1 , . . . , xn has the form
a1 x1 + a2 x2 + a3 x3 + + an xn
where the numbers a1 , . . . , an R ar
Three.VI Projection
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Orthogonal Projection Into a Line
Project a vector into a line
This shows a figure walking out on the line to a point ~p such that
the tip of ~v is directly above them, w
One.III Reduced Echelon Form
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Gauss-Jordan reduction
Pivoting
Here is an extension of Gausss Method with some advantages.
Example Start as usual with elimination operations to get echelon
for
Three.V Change of Basis
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Changing representations of vectors
Coordinates vary with the basis
Consider this vector ~v R3 and bases for the space.
1
1
0
0
1
0
1
~v = 2
E3 = h0 , 1 , 0i B
Linear Algebra Proofs
Below are several proof techniques that you should KNOW how to apply by the end of 3191 . . . this means that
any of these is fair game for the final exam. Each one below comes with several examples.
1. Let H be a subset of a vector
Spaces and their subspaces
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Real three-space
Subspaces of R3
The next slide shows a smaple of subspaces of the vector space R3 :
the entire space, planes, lines, and the trivial subspace. Sub
Angles and Eigenvectors
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Lines transform to lines
Lines go to lines
Consider a real space transformation t : Rn Rn . A defining
property of linear maps is that t(r ~v) = r t(~v).
In a real sp
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Pag
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Outline the roles of nitrate ions and of magnesium ions in plants
Ions
Nitrate, NO3-
Some roles in plant
Nitrate is used to help
make amino acids;
organic bases, e.g.
adenine; proteins;
nucle
The action of plane transformations
Linear Algebra
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Transformations of R2
Lines go to lines
Consider a real space transformation t : Rn Rn . A defining
property of linear maps is that t(r ~v) = r t(~v).
In
San Marino Policy
LAU & WU
AFF
CUBA PLS
STATE QUALS 2014
LAY AC
1AC EMBARGO - STATES
We affirm resolved: The United States federal government should substantially increase its economic
engagement toward Cuba, Mexico or Venezuela.
This topic requires the a
Ideology/epist indicts
1. We only look at the env in instances of eco destruction when it threatens humans. For
example, we only look at Flint because there is a water crisis, and we only look at it in
contenxt ofg how humans portray those threats in the
Nuclear Renaissance AC
Part 1 is Framing
Energy policy making must be understood in a social context requiring situating nuclear in the
broader context of society and the economy to understand that traditional cost benefit
assessment relies on flawed tech
Framework
I affirm
This debate should center on tangible policies that address oppression.
Curry 14, Tommy, The Cost of a Thing: A Kingian Reformulation of a Living Wage Argument in the 21st Century, Victory Briefs, 2014,
Despite the pronouncement of deba
AT Util
AT Util Dump
Each type of pleasurethe pleasure of sleeping, the pleasure of eatingis qualitatively
different, so we cant quantify and compare pleasures under consequentialism.
2. Aggregation is nonsensicalassessments of moral harms must reference
Reptoids Affirmative
The Human Species is bio-prospected to feed an Ancient Alien Race
called the Anunnaki which is the root cause of all forms of violence
Lewis and Kahn 05 (Tyson Lews and Richard Kahn, associate professor of art education in
the Departm
Nuclear power is unpopular for the first time since 94 energy prices, not
meltdowns
Riffkin, 3/6/16, (Gallup Poll, For First Time, Majority in U.S. Oppose Nuclear
Energy, http:/www.gallup.com/poll/190064/first-time-majority-oppose-nuclearenergy.aspx)
For
Part 1 is Framework:
I affirmall brackets for offensive language or clarity.
Welcome to the world where the politics of domestic terrorism has corrupted the
very foundations of democracy, a world where the police you are trying to protect
kill countless y
1. Impact turn- militarism uses police and state violence to fracture communities so that they kill
each other and themselves, which prevents them from implementing the alt. That means the aff
is a prerequisite to the solvency of the alternative.
2. Perm-
1
A. Interpretation: If the affirmative:
1. Does not solely defend the implementation of
the resolution as policy
2. Specifies a role of the ballot of challenging
discourse within the debate space such as
using counter-narratives to demystify the
power of
1NC
2AC
ejndpoitn fo tyhge 1ac is antibalck
legal sturcutres and society
Bar 13
perm - give animla rights is
the end of the world
ontological stance of the world
animals have less rights than
blacks
blackness
barely get in trouble
no human suffering
balck
Calculus
Section 2.2 Velocity and Acceleration
1. The position equation for the movement. of a particle is given by s = (12 ~ 1)3 when s is
measured infect and t is measured in seconds. Find the acceleration at two seconds.
2. Suppose the position equatio
CHAPTER I'-" I"
Composition and
Decomposition of
Functions
Composition
m) = Vi,
f(x"') = Vx4 + 1,.
f(sinx) = .V sinx + 1,
d=vd+L
f(whatever) = V whatever + 1.
and
Get it? Got it? Good!
3 Let f(x) = 2 + 2x + a.- and g(x) = x3. Then what is f(g(x)?
Solu
Calculus
Name_
4.6 Related Rates
Date_ Period_
8 b2305193o lK0uCt5ai FSHopfitcwkadr9ee MLBL1Cv.0 h cA5lrlx 8rzi8gThztZs9 2rJejsqeprTvCeVdy.w
Solve each related rate problem.
1) A spherical balloon is deflated so that its radius decreases at a rate of 4 cm
CALCULUS
WORKSHEET ON OPTIMIZATION
Work the following on notebook paper. Write a function for each problem, and justify your
answers. Give all decimal answers correct to three decimal places.
1. Find two positive numbers such that their product is 192 and
1. Suppose you are trying to prove lim (4x 1) = 11. Given > 0, what value must be in
x3
order to satisfy the formal definition of the limit? (No need to show formal proof)
Solutions to Continuity Exercises
1.
=
4
2. (a) No
(b) Yes, let f (1) = 1
(c) Yes,
Math 5A
Fall 2016
Study Guide for Exam 2
DISCLAIMER: This study guide is not exactly like the next exam. It is a helpful way
to practice the concepts you will need to master for the next exam.
1. The limit represents the derivative of some function f at s