Explain why pointwise convergence do not preserve differentiation and integrability. (Unlike uniform convergence)

Let “ ·n” be multiplication modulo n, and consider the set Un = { [a] ∈ Zn | there is a [b] ∈ Zn with [a] ·n [b] = [1]}

(a) Show that (Un, ·n ) is a group.

(b) Write down the Cayley table for U5. Hint: |U5| = 4.

(c) Write down the Cayley table for U12. Hint: |U12| = 4.

Prove that any amount of postage greater than or equal to 14 cents can be built using only 3-cent and 8-cent stamps

Suppose that W1 and W2 are subspaces of V and dimW1<dimW2. Prove that there is a nonzero vector in W2 which is orthogonal to all vectors in W1.

Please show all work and calculations neatly!

no code allowed!

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Using Simpson's Rule, verify that the weight w1 equals 4h/3 by integrating the appropriate Lagrange basis function

You will write a short (less than two pages double-spaced) paper. The paper may include diagrams, graphs, or screenshots.

Your boss has given you the following data table. The table shows the temperatures y (in degrees Farenheit) in a city over a 24-hour period. Let x represent the time of day, where ? = 0 corresponds to 6 a.m.

time, x Temperature y

0 34

2 50

4 60

6 64

8 63

10 59

12 53

14 46

16 40

18 36

20 34

22 37

24 45

These data can be modeled approximately by the polynomial function,

?=0.026?3 −1.03?2 +10.2?+34, 0≤?≤24

(a) Use a graphing utility (calculator or some on-line app) to create a scatter plot of the data. Then graph the polynomial in the same viewing window.
(b) What is your informed opinion about how well the function fits the data?
(c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period.

(e) Write a memo to your boss explaining your steps and your answers in (a) through (d). Include any graphs necessary to explain yourself.

Solve the equation below for y(t):

y''+2y'-3y=8u(t-3): y(0) = 0; y'(0)=0

Find the number of passwords that use each of the digits 3,4,5,6,7,8,9 exactly once. IN how many of the passwords:

1. are the four odd digits consecutive?

2. are no two odd digits consecutive?

3. are the first three digits even?

4. are the three even digits consecutive?

the matrix A=[-5,1;-21,5] has eigenvalues Г1=-2 and Г2 = 2 the basis of the eigenspace v1=[1,3] v2=[1,7]
find the invertible matrix S and diagonal matrix D such that S^-1 AS=D
S=
D=

Image:

bit.ly/2RvpGag

The following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets.

(a) Use regression to find a quadratic model for the data. (Round the regression parameters to two decimal places.)
R =

(b) Calculate

R(65).

(Round your answer to two decimal places.)

R(65) =

Explain what your answer means in practical terms.

Commercial vehicles driving at night on urban streets at  miles per hour have traffic accidents at a rate of  per 100,000,000 vehicle miles.

(c) At what speed is vehicular involvement in traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Round your answer to the nearest whole number.)
mph

Let x be a fixed positive integer. Is it possible to have a graph G with 4x + 1 vertices such that G has a vertex of degree d for all d = 1, 2, ..., 4x + 1? Justify your answer. (Note: The graph G does not need to be simple.)

The matrix A=[-2,0,2;0,-4,0;-2,0,-6]
has a single eigenvalue=-4 with algebraic multiplicity three.
a.find the basis for the associated eigenspace.

b.is the matrix defective? select all that apply.
1. A is not defective because the eigenvalue has algebraic multiplicity 3.
2.A is defective because it has one eigenvalue.
3.A is defective because geometric multiplicity of the eigenvalue is less than the algebraic multiplicity.
4.A is not defective because the eigenvectors are linearly dependent.