1.a
Consider the problem of cubic polynomial interpolation
p(xi) = yi, I = 0,1,23
with deg(p) 3 and x0, x1, x2, x3 distinct. Convert the problem of finding p(x)
to another problem involving the solution of a system of linear equations.
b) Express the syst
February 12, 2015 A
Name:
I have neither given nor received ai on t 's exa
(Signature / Date)
Instructions:
0 If you look at someone elses paper or talk during the exam or you are caught using unauthorized
material (like solved problems), you will be
If / ('Qlflffl/ g i (cfw_)(05)(OS)(/S) zigzag;
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Math 4329, Test II (&\
Name "1&7 _
1. If P3(x ) is the cubic polynomial that interpolates to f(x cat
as = 0, 0.1, 0.2, 0.3, nd a reasonable bound on the error at x 60 15.
@&)3(4 "5 )0?) (X0)cfw_><*O!)(
3
Math 4329, Test I (g)
1. Let T3 (3:) be the Taylor polynomial of degree 3 which matches f (m), f (11:), f(:c)
and f(x) at &= 0, where f(:I:) = 003(3x). Find the best possible
bound on
max_0.15xso,1|T3($) f($)l S
2. IEEE double precision oating point
Problem 1. Find the binary and double precision floating point expressions for the following numbers:
(a) 8
Find the binary representation of 8 as follows:
82=4
42=2
22=1
12=0
R=0
R=0
R=0
R=1
a0
a1
a2
a3
=0
=0
=0
=1
Thus, in binary, 8 = (1000)2 = 1.0 23 .
Homework 1
Numerical Analysis (CMPS/MATH 305)
Hani Mehrpouyan
Homework 1 Solution
Q UESTION 1 (5 POINTS )
Produce the linear and quadratic Taylor polynomials for the following cases. Graph the function and these Taylor
polynomials.
a) f (x) =
x, a = 1
b)
Homework 2
Numerical Analysis (CMPS/MATH 305)
Hani Mehrpouyan
This homework is due by Thursday April 25th 2013
Q UESTION 1 (5
POINTS )
Using MATLAB find the binary double precision IEEE floating-point expressions for the following numbers:
a) 8
b) 0.5
Q U
Computational methods, Hw 4 (due 3/5)
(At least one of the problems will be graded)
Example 1 (4.1/1) Given the data points (0, 2), (1, 1), find the following:
(a) The straight line interpolating this data, (b) The function f (x) = a + bex
interpolating t
Consider the following. HINT [See Examples 13.]
A letter is chosen at random from those in the word Mozart; the letter is neither a nor m.
which ofthe following sets of elements are included in the sample space? (Select all that apply.)
8 m
El
CEEEEE
HI
The map heiow shows the percentage change in homing pricg from June 2010 to June 2011 in each of nine regions (0.5. CEI'SLS divisions).
You are choosing a region ofthe country to move to. Describe the event Ethat the region you choose saw a decrease in
Corsider the following. HINT [See ExamplE 173.]
You are considering purchasing either a domestic car, an imported car, a van, an antique carr or an antique truck; you do not buyr a car.
which ofthe following sets of elements are included in the sample spa
The table shows the performance of a selection of 100 stocks alter one year. (Take 5 to he the set of all stocks represented in the table. If a stock stayed within 20% of its original value, it is classied as
'unchanged'.)
Comp
Let W be the event that you will use the book's Website tonight, let I be the event that your math grade will improve, and let E be the event that you will use the Website every night. Express the given event in
wmbals.
Ether ynu will LEE the Website ever
The following table shows the frequency of outcomes when two distinguishable coins were tossed 4,400 times and the uppermost faces were observed. HINT [See Btample 2.]
Olltcnme HH HT TH "IT
Frequency 1,200 1,050 1,300 050
What is the relative frequenw t
In a survey of 390 Latin music downloads, 150 were regional cfw_Mexican/Teiano), 115 were pop-rock, 75 were tropical cfw_salsalmerengueycumbiaybachata), and 50 were urban [reggaeton). Calculate the following
relative frequencia. (Round your arswers to two
Corsider the following. (Assume that the coins are d'Btingu'Bhahle and that what '6 observed are the fang or numbers that face up.) HINT [See Examples 1-3.]
Three coins are tcased; the result '5 at mcst one head.
which of the following sets of elements ar
Suppose two dice [one red, one green) are rolled. Consider the following events. A: the red die shows 2; E: the numbels add to 5; C: at least one ofthe numbels is 2; and D: the numbels do not add to 10.
Expriss the given event in symhok. HINT [See Example
Consider the Following. (Assume that the dice are distinguishable and that what is observed are the numbers that Face up.) HINT [See Exampl 1-3.]
Two distinguishable dice are rolled: the numbers add to 6.
Dacribe the sample space S of the experiment. (Sel
1206 Chapter [2 Vector- Valued Functions
55. r(I) = 6 cos Ii + 3 sin tj 57.
(a) v(I) = r'(I) = 6 sinti 3 costj
ll v(I) I] = +336 sin2 I + 9 cos2 I
=3J4s sin I +cos t = 3J3sin t +1
21(1) = v(t) = 6 cos Ii 3 sin Ij
58.
J.
t
I'-
M.
It.
% ~
-8 i ' I
-4
-5
5
Sec/ion 13.3 lDariticJl Derivalives 1275
80. Given that f(x, y) is continuous, then ( gin; I)f(x, y) = f(n, b) < 0, which means that for each a > 0, there corresponds
my > a. J
a 6 > Osuch that |f(x, y) f(a,b)| < ewhenever
0< (xa)2+(yb)2 <5.
Let g = |
CHAPTER 13
Functions of Several Variables
Section 13.1 Introduction to Functions of Several Variables
1. No, it is not the graph of a function. For some values of x
(0, 0), there are 2 z-values.
and y (for example, (x, y) =
2. Yes, it is the graph of a fu
W (II1E 2,11% 1;. I; -. cfw_3314.714
cfw_9113;3 IU- 1?5 I
1222 Chaplez'JZ Veclor- Valued Functions
76. Let T(I) = cos i + sin j be the unit tangent vector. 78. Using a = aTT + aNN, T x T = 0, and T x N = I,
Then you have:
, dT _
T(t)=(it_ vxavllTx(a1-T+0N
Math 2313
Exam III: Spring 2017
Score:
/100
Hints for Selected Problems
Problem 1. (10 points) The pressure P , volume V , and temperature T of a van der Waals gas with n
molecules (n is constant) are related by the equation
where a, b, and R are constant
Math 2313
Exam II: Spring 2017
Review
Each problem on the exam will be worth 10 points. Some problems may have 2 (or more) parts, in which
case the points will be adjusted accordingly. The exam is out of 100 points with one bonus problem that is
worth 10
El Paso, TX202 Stanton Dr.Mesita Elementary
Sarah Villa
ELED 4310
Planning,
Teaching, and
Assessing
Culturally and
Linguistically
Diverse
Students
Promoting diversity is a
goal shared by many in
American colleges and
universities, but actually
achieving t