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Displacement and Definite Integrals
1. Let f (x) = x2 . Find the value of the sum
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f (j).
j=1
2. A ball is thrown vertically so that its velocity is v(t) = 32 32t, where t is
measured in seconds and v is in feet per second. The graph
Biol&242
Endocrine System Homework
Due Wednesday 1/15/14 (at the beginning of class)
Do NOT wait until the last minute! This is a long and involved assignment and
may take several hours to complete.
ONLY TURN IN THE ANSWER SHEET (pages 15 and 16)
You may
3/31/2015
Data to Knowledge
Chapter 1: Statistical Basics
The scientific path from data to
knowledge.
Slide set to accompany "Statistics Using Technology" by Kathryn Kozak (Slides by David H Straayer) is
licensed under a Creative Commons Attribution-Share
The table summarizes results from 982 pedestrian deaths that were caused by
automobile accidents.
Pedestrian Intoxicated?
Driver
Intoxicated?
Yes
No
Yes
56
82
No
287
557
If one of the pedestrian deaths is randomly selected, find the probability that the
p
CHAPTER
9
Nonlinear Dierential Equations and
Stability
9.1
2.(a) Setting x= ert results in the algebraic equations
5r
3
1
1r
1
2
=
0
.
0
For a nonzero solution, we must have det(A r I) = r2 6 r + 8 = 0 . The roots of
the characteristic equation are r1 = 2
CHAPTER
10
Partial Differential Equations and
Fourier Series
10.1
1. The general solution of the ODE is y(x) = c1 cos x + c2 sin x . Imposing the
first boundary condition, it is necessary that c1 = 0 . Therefore y(x) = c2 sin x .
Taking its derivative, y
CHAPTER
7
Systems of First Order Linear
Equations
7.1
1. Introduce the variables x1 = u and x2 = u . It follows that x1 = x2 and
x2 = u = 2u 0.5 u .
In terms of the new variables, we obtain the system of two rst order ODEs
x1 = x2
x2 = 2x1 0.5 x2 .
3. Fir
CHAPTER
11
Boundary Value Problems and
Sturm-Liouville Theory
11.1
1. Since the right hand sides of the ODE and the boundary conditions are all zero,
the boundary value problem is homogeneous.
3. The right hand side of the ODE is nonzero. Therefore the bo
CHAPTER
2
First Order Differential Equations
2.1
5.(a)
(b) If y(0) > 3, solutions eventually have positive slopes, and hence increase without bound. If y(0) 3, solutions have negative slopes and decrease without
bound.
R
(c) The integrating factor is (t)
CHAPTER
3
Second Order Linear Equations
3.1
1. Let y = ert , so that y 0 = r ert and y 00 = r2 ert . Direct substitution into the
differential equation yields (r2 + 2r 3)ert = 0 . Canceling the exponential, the
characteristic equation is r2 + 2r 3 = 0 . T
CHAPTER
6
The Laplace Transform
6.1
3.
The function f (t) is continuous.
191
192
Chapter 6. The Laplace Transform
4.
The function f (t) has a jump discontinuity at t = 1, and is thus piecewise continuous.
7. Integration is a linear operation. It follows t
CHAPTER
8
Numerical Methods
8.1
2. The Euler formula for this problem is yn+1 = yn + h(5 tn 3 yn ), in which
tn = t0 + nh . Since t0 = 0 , we can also write yn+1 = yn + 5nh2 3h yn with
y0 = 2 .
(a) Euler method with h = 0.05 :
tn
yn
n=2
0.1
1.59980
n=4
0.
CHAPTER
5
Series Solutions of Second Order
Linear Equations
5.1
1. Apply the ratio test:
lim
(x 3)n+1
n
|(x 3)n |
=
lim |x 3| = |x 3| .
n
Hence the series converges absolutely for |x 3| < 1 . The radius of convergence
is = 1 . The series diverges for x =
CHAPTER
4
Higher Order Linear Equations
4.1
1. The dierential equation is in standard form. Its coecients, as well as the
function g(t) = t , are continuous everywhere. Hence solutions are valid on the
entire real line.
3. Writing the equation in standard
CHAPTER
1
Introduction
1.1
1.
For y > 3/2, the slopes are negative, therefore the solutions are decreasing. For
y < 3/2, the slopes are positive, hence the solutions are increasing. The equilibrium
solution appears to be y(t) = 3/2, to which all other sol
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Math 152
Spring 2013 _
Show all necessary work to receive credit. _
Answers without supporting work receive little to no credit.
Quiz #2
.0
You may use your graphing calculator.
1. Suppose that C(t) rep
Math152 Quiz #2 ' Name: 5MC -
Winter2014. 5 Score: /10
Show ail‘necessary work to receive credit.
Answers without supporting work receiVe little to no credit.
1. Using the graph of the derivative below to answer the questions.
b) List the following in i
Math 152 Quiz 5 I Name:
Show all necessary work to receive credit.
1. Write a definite integral representing the area of'the region bounded by:
y = ﬂ and y = x using horizontal slicing as shown:
b) Use your calculator to approximate the volume of this s
Math 152 Quiz #1 Name: 5 D‘ﬂ ~
Fall 2014 ' 7
Show all necessary work to receive credit.
Answers without supporting work receive little to nolcredit.
Do not use your graphing calculator ’s capacity. You may use your calculator as if it is a
scientific calc
Math 151 Fall 2013 Exam #3 Name:
Instructor Tran
Show all necessary work and answers to receive credits. _
Remember to Show all supporting work in an organized manner and notjust the answer.
N0 GMPHING CALCULATOR
6. Find constants a and b in the functio
Math 151 Name:
Fall 2013
Quiz #6
Show all necessary work to receive credit.
Answers without supporting work receive little to no credit.
I 1. .
51) Find the linear approximation to 3Vx + 1 near x = 0.
.n_—
.—
‘ Ame/W 32mm: .09, to:
o) Is your approximatio
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Math 151 Fall 2013 Exam #2 _ Name: 5
Instructor Tran Part 1 Score:
Show all supporting work in an organized manner to receive credit. '
Calculator: TI-84 or TI-83 allowed.
1. Assume that we do not know how to ﬁnd the derivative to the following fun