Finding the Volume of a Potato
Mackenzie Reed and Mikayla Holmes
Introduction
Consider the integral from a to b of A(x)dx. This could be used as a numerical approach to find
the volume of a three-dimensional object. Now consider the three-dimensional obje
Attack of the Cane Toads: Invasive Species Control & Modeling
Mackenzie Reed (0696567)
Mikayla Holmes (0616676)
Professor Kavanagh
Section 2
Introduction
Cane toads have been invading Australia wreaking havoc on the habitats and community for
several year
MA132
Final exam
Review
Area between curves
Partition into rectangles!
Area of a rectangle is
A = height*base
Add those up!
(Think: Reimann Sum)
n
f ( x ) g ( x ) x
i
i 1
i
n
f ( x ) g ( x ) x
i
i
i 1
b
f ( x) g ( x) dx
a
For the height, think top bott
ROLLER COASTER DESIGN
Emilee Carpenter
1. INTRODUCTION
A roller coaster is to be built under certain specifications. The ride, themed around space
travel, will replicate the feeling of weightlessness, or 0-g, as it goes over the hills. A camera
is to be p
Antarctic Ice
Impact of Changing Ice
Cover on Solar Heat
Absorption
Emilee Carpenter ID: 0583267, Lecture Section 02
Katelyn Graham ID: 0583261, Lecture Section 02
1. Introduction
The long term effects of polar ice depletion can be seen on a global scale.
MA330-F16
Quiz 02
Q (Sec at 11am):
The attached figure shows a city block with
flows of cars through inbound and outbound
one-way streets. The number of cars per hour is
written out next to every arrow. Traffic through
some streets (labeled by letters A,
MA330-F16
Quiz 04
Q (Sec at 11am):
Compute the Fourier coefficients a0 , an , bn of the periodic function given by the graph.
(a) Determine the fundamental period P the associated angular frequency of the function and
indicate it on the graph.
(b) Can you
MA330-F16
Quiz 05
Q (Sec at 11am):
(a) Explain the relationship between the Fourier transform f( ) and the spectral density of the function f (t).
(b) Sketch graphs of any two functions f (t), g(t) such that | f( )| = | g ( )| for all , but whose phases o
MA330-F16 Quiz 07
Q 11am:
Consider a PDE for the function u( x, y, t) evolving on the spatial domain D = [0, 1] [2, 4].
(a) Sketch the spatial domain D.
(b) Describe, in mathematical terms, the boundary D of the spatial domain D.
(c) Describe the differen
MA330-F16 Quiz 06
If L[ f ] = F (s) then
L[ f (t)e at ] = F (s a)
L[ f 0 (t)] = sF (s) f (0)
Rt
L[ 0 f ( )d ] = F (s)/s
L[ f (t a)u(t a)] = F (s)e as ,
where u(t) is the unit step function at t = 0.
Unit step L[u(t)] = 1/s
Dirac L[(t)] = 1
Q 11am:
(
MA330-F16 Quiz 08
Q 11am:
(a) Explain the main mathematical difference between the PDE for the heat flow (heat equation) and the PDE
for the mechanical vibrations (wave equation) for the function u(t, x ) evolving in time and 1D space?
(b) The ODE F 00 (
MA330-F16
Quiz 03
Q (Sec at 11am):
A system of ODEs for the vector of variables x (t)
1
x = 0
0
is given in the matrix form:
0
0
2 1 x.
1 2
h1i
One eigenvalue of the associated matrix is 1, with eigenvector 0 .
0
(a) Find the remaining two eigenvalues of
MA330-F16
Quiz 01
Q1 (Sec at 11am):
A cart (m = 1) is connected to an anchor by a parallel connection of a damper (c = 2) and a spring
(k = 3).
(a) Find the ODE for the position of the cart x using the balance of the forces. Justify your solution
via a fr
(9) Graph the position, velocity, and acceleration functions for the rst 8 s.
V
(h) When, for 0 s t < no, is the particle speeding up? (Enter your answer in interval notation.)
When, for 0 S t < co, is it slowing down? (Enter your answer in interval
A particle moves according to a law of motion 5 = f(t), t z 0, where t is measured in seconds and s in feet.
r(t)=t39t2+ 15:
(a) Find the velocity at time t.
(b) What is the velocity alter 2 s?
V(2) = \ lt/s
(c) When is the particle at rest?
t = s (smal
Differentiate the following function.
y: 5+sinx
5x+cosx
Need Help? i i
Find the derivative of the function.
y= 2+6e4"
Need Help? i i
Find the derivative of the function.
y = 10312
Y'=
Need Help? i i
Show that f is continuous on (eo, an).
x)=cfw_1-x2 ifxs1
ln(x) ifx > 1
0n the interval (ce, 1), f is 1 -Select- a function; therefore f is continuous on (oo, 1).
On the Interval (1, no), f is 1 -Selecl- a function; therefore f is continuous on (1, s
Find dy/dx by implicit differentiation.
Xzyz + x sin y = 7
y'=
Need Help? i i i
Find dy/dx by implicit differentiation.
x/Jry = 6 + Xzy
Need Help? i i
Use logarithmic differentiation to nd the derivative of the function.
y = (sin 9X)X
Need
The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price ofp dollars per pound is Q = F(p).
(a) What is the meaning of the derivative f '(7)?
O The rate of change of the price per pound with respect to the quantity o
If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is
A(x) = All.
X
(a) Find A'(x).
O A'(x) = M 'XX X
o W) = W
O A'(x) = M
Why does the company want to hire more wo
Math 339 Midterm Review
(1) Given the matrix
1 0 0
A = 0 1 1 .
0 1 1
(a) Find the eigenvalues and eigenvectors.
(b) Diagonalize A, that is, find matrices P and D such that A =
PDP1 .
(c) Compute A7 using the decomposition in part b.
(2) (a) Find the LU de
Math 339 Quiz 3 Redo
Let
e1 =
3
0
, e2 =
0
1
, y1 =
2
5
, y2 =
1
6
and let T : R2 R2 be a linear transformation that maps e1 into y1 and
maps e2 into y2 . Find the images of
7
x1
and
.
2
x2
1
MA 180* Fall 2010* Exam 1
Name _
_ of 80 points
There are twenty questions on this exam worth four points each. Partially correct answers may receive
partial credit. Put all answers in the answer column. Only the answers in the box will be graded. Use
scr
MA132: Calculus II Exam 2 (14 March 2002)
Name: Student Number:
(12) Problem 1. For the region enclosed by the curves y 2 = 4x + 16 and 2x + y = 4: (a) Sketch the region (label intersection points).
t (0, 4) 6 A
y
ANSWER: To plot rst curve (quadratic), nd
MA132: Calculus II Exam 3 (18 April 2002)
Name: Student Number:
(20) Problem 1. Test each series for convergence. Show your work and cite the test(s) used. (a) 8n n=0 (n + 1)!
ANSWER: Use the Ratio Test: an+1 an 8n+1 8n+1 (n + 1)! 8 (n + 2)! = = = 0=L<1 n
MA132: Calculus II Exam 3 (18 April 2002)
Name: Student Number:
(20) Problem 1. Test each series for convergence. Show your work and cite the test(s) used. (a) 8n n=0 (n + 1)! 1 2 n=2 n [ln(n)]
(b)
(20) Problem 2. Test each series for convergence. Show
MA132-Calculus II Exam 2 13 June 2006
Instructions: Show your work.
Name: Student Number:
Answers without sufficient justification may not receive full credit. No books, notes, or calculators. Time limit: 90 minutes. Some integrals which might help: sec(
MA132Calculus II Exam 2 (13 June 2006)
Name: Student Number:
(12) Problem 1. Consider the region between the curves y = 2 x and y = x2 for 0 x 2. (a) Sketch the region. Label the axis scales and any points of intersection. ANSWER: y 6 4 3 2
d d
1
d d d d