a [0 nd an expression for the area under
enilitt ~ . .
Use Ff as H mm Do not evaluate the limit.
SECTION 5.2 THE DEFINITE INTEGRAL 371
that the n rectangles representing Rn L. can be reassem-
bled to form a single rectangle whose area is t
SERIES - CONVERGENCE TESTS - Note: an
Test for Divergence
WHAT IT STATES
a = ar
if r < 1 an converges to S =
if r 1 an diverges
Don't confuse p-series with geometric ser
Note the version displayed at the bottom of each page. Watch
for changes to this version at the Exams section of the website.
MATH 2212 Fall 2016
Exam 1 Review Set
A. Use the
In parts A-E, evaluate the integral.
u 3 + u 2 ) d
Math 2212, Test 1
1. Find the derivative of each of the following (6 points each):
(a) f (x) = sin(x2 )ecos(x)
(b) g(x) = log5 ( x)
2. Use logarithmic dierentiation to nd the derivative of (8 points):
f (x) =
(2x + 1)(2x + 2)(2x + 3)
Math 2212, Test 3
No calculator allowed. Always justify your work or no point will be earned
on the problem.
1. Find the limit of the following sequences (6 points each):
(a) (n + 3)1/2n
(b) ln( 3n2+1 )
(c) (|t| + n )n
2. Use LHpi
Calculus 2, Fall 2013, Test 4
December 1, 2013
You must show all your work to receive full credit for a question.
1. Expand x3 2x2 + x 1 in powers of x + 1 (10 points).
2. Expand 3x in powers of x 1. You must write the genera
Volume 2, Number 3, August 2005
MODELING MULTICELLULAR SYSTEMS USING
T. J. Newman
Department of Physics & Astronomy, and School of Life Sciences,
function dU = net(t,U)
%First have to name the function. dX and X are vectors.
X = reshape(U,[1 2]);
0X = [dx,dy]
dX(:,1) = -beta.*X(:,1).*X(:,2);
dX(:,2) = (beta.*X(:,1).*X(:,2) - (nu.*X(:,2);
0X(:,1) = c.*(X(:,2)+X(:,
%Give values for constants beta and nu.
beta = 0.52;
nu = 54.1889;
t0 = 0;
tf = 1000;
%Initial vector (initial conditions, e.g., x0=0.1 and y0=0.3) Y0=[x
Mathematical Biology 4010/6010 Fall 2012
Research Project: Smallpox
Max points: 100
Due Tuesday, November 27
An outbreak of smallpox in Abakaliki in southeastern Nigeria in 1967 was reported
by two researchers Bailey and Thomas. People living ther
2211 Spring 2009
Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Use a new page for each problem. Do problems in sequential order. Please use pencil. When finished, place this
2211 Fall 2008 Test 1
Show all necessary work in your blue book. Please use a different page for each complete problem. Incorrect or non-work will not receive credit. When finished, please place this question paper inside your blue book and turn it
Study Guide Chapter 42 The Immune System
What materials, tissues, and organs make up the non-specific responses to infection?
How is the lympthatic system involved with both specific and non-specific defense?
Hematopoetic stem cells produce multiple cell
33.1 What Is a Deuterostome?
Deuterostomes are triploblastic, coelomate animals with internal skeletons.
33.1 What Is a Deuterostome?
Living deuterostomes comprise three clades: Echinodermssea stars, sea urchins, and their relative
32 Protostome Animals
32.1 What Is a Protostome? 32.2 What Features Distinguish the Major Groups of Lophotrochozoans? 32.3 What Features Distinguish the Major Groups of Ecdysozoans? 32.4 Why Are Arthropods So Diverse?
32.1 What Is a