Polytechnic Institute of NYU MA 1024/1324
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Worksheet 11
1
2
(1) Find the
Math 354 Summer 2004
Homework #5 Solutions
Please write your answers on a separate sheet of paper, and include at least some intermediate steps
and English words.
This homework covers sections 3.1-3.4.
1
Consider the linear programming problem
Maximize z
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 12
1
2
(1) Find the
1
Chapter 6 Problem Set
Chapter 6
PROBLEMS
1.
[E, None, 4.2] Implement the equation X = (A + B) (C + D + E) + F) G using complementary CMOS. Size the devices so that the output resistance is the same as that of an inverter
with an NMOS W/L = 2 and PMOS W/
Solid State Physics
Homework Set 1
Solutions
January 30, 2002
1
Ibach and L th Problem 1.1
u
The Madelung constant is a specic example of a summation in Solid-State Physics generally
known as a lattice sum. For the linear chain of ions it is more instruct
Homework Solutions for Math 4800
Tim Anderton, Charlotte Cannon, Miles Fore, Brian Hunt, Jason Meakin, Onyebuchi Okoro, and Alex Pruss University of Utah Spring 2008
2
Chapter 2
2.2.1 (Miles) The ordering of the vertices of a knot is very important. If th
Design of Algorithms - Homework I (Solutions)
K. Subramani
LCSEE,
West Virginia University,
Morgantown, WV
cfw_ksmani@csee.wvu.edu
1
Problems
1. Consider the following algorithm for sorting an array of n numbers.
Function A RRAY-S ORT(A, n)
1: for (i = 1
EE364b
Prof. S. Boyd
EE364b Homework 2
1. Subgradient optimality conditions for nondierentiable inequality constrained optimization. Consider the problem minimize f0 (x) subject to fi (x) 0, i = 1, . . . , m,
with variable x Rn . We do not assume that f0
EE364a, Winter 2007-08
Prof. S. Boyd
EE364a Homework 5 solutions
4.15 Relaxation of Boolean LP. In a Boolean linear program, the variable x is constrained
to have components equal to zero or one:
minimize cT x
subject to Ax b
xi cfw_0, 1,
(1)
i = 1, . . .
MAT 444 H. Barcelo Spring 2004
Homework 1 Solutions
Section 2.1 Questions: 5. Assume that the equation xyz = 1 holds in a group G. Does it follow that yzx = 1 ? That yxz = 1 ? Answers: a) If xyz = 1 then yz = x 1 and yzx = x 1 x = 1
b)
If x y z = 1 but G
Math 208 Solutions to Homework Assignment 8
ez
:
(z +1)2
p205. 2. Let f (z ) =
We know that ez has a Taylor series expansion at z =
ez = e
1 z +1
e
thus we obtain
ez
=e
2
(z + 1)
1
1
X (z + 1)n
n!
n=0
1
=e
1;
1
X (z + 1)n
n!
n=0
2
3. We want to nd a repre
CHAPTER 24 HOMEWORK SOLUTIONS
24.3.
IDENTIFY and SET UP: It is a parallel-plate air capacitor, so we can apply the equations of Sections
24.1.
Q
Q 0.148 10 6 C
EXECUTE: (a) C
so Vab
604 V
Vab
C
245 10 12 F
12
3
PA
Cd 245 10 F 0.328 10 m
0
so A
9.08
CALCULUS I SELECTED HOMEWORK SOLUTIONS
Section 2.1. (8) The slope of the tangent line to the graph of y = g(x) = 9 x2 at the point (2, 5) is given by g (2) = lim g(2 + h) g(2) h0 h 9 (2 + h)2 5 = lim h0 h 9 4 4h h2 5 = lim h0 h = lim 4 h
h0
= 4 So the slo
Math 331.5: Homework 12
Solutions
1. Consider the dierential equation y + 5y 6y = 0.
(i) Find a fundamental set of solutions of the dierential equation.
The characteristic equation is r2 + 5r 6 = 0. Factoring,
r 2 + 5r 6 = 0
(r 1)(r + 6) = 0
r=1
or
r = 6
ECE 275A Homework #3 Solutions
1. Proof of (a). Obviously Ax = 0 y , Ax = 0 for all y . To show suciency, note
that if y , Ax = 0 for all y , then it must certainly be true for the particular value of
y = Ax. This yields Ax 2 = 0 Ax = 0.
Proof of (b). Let
Polytechnic Institute of NYU MA 1024
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Worksheet 2
1
2
(1) Form the compo
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 3
1
2
(1) Determine whether th
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 4
1
2
(1) Are the functions co
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 5
1
2
(1) Given the graph
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 6
1
2
(1) Where are
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 7
1
2
(1) Find the deriva
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 8
1
2
(1) Find the
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 9
1
2
(1) Find the derivative.
Polytechnic Institute of NYU MA 1024/1324
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Worksheet 10
1
2
(1) A balloo
MATH 113 HOMEWORK 6 SOLUTIONS
1. Abelian Groups
Problem 1.1 (Linear Algebra of Abelian Groups, Part I). Let A be an
abelian group, and suppose that cfw_a1 , . . . , an A is a generating set for A.
(1) Show that for i = j and k Z, the set cfw_a1 , . . . ,
Polytechnic Institute of NYU MA 1024
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Worksheet 1
Your signature: (1) Fi